Driving to Denali National Park is about the same distance one way (250 miles) as if you were to driving to Homer (220 miles) from Anchorage...
I would highly recommend Homer over Denali National Park as Homer is the most majestic place on the Kenai Peninsula in my opinion, you can't go wrong driving anywhere else on the Kenai Peninsula for that matter either in a rental car for a sightseeing getaway.
Girdwood, Portage-Whittier, Hope, and Seward are very easy one day driving round trips back to Anchorage while stopping to see other sites in between without getting tired (or not getting too tired), however to really enjoy Homer I would find some overnight lodging just so you remain refreshed to enjoy more of the return driving trip back to Anchorage while enjoying a few more extra stops along the way compared to a day trip to Homer and back in one day.
Although you can see Homer and drive back to Anchorage in one full day as I had done the first time in 1990 at a young age of 24, I was sure real tired when I made it back to my destination in Anchorage.
Whittier is one of the few places along the entire road system in Alaska I have not been to, before the access road put in place Whittier was only accessed by rail, however the drive there and a boat tour thru the surrounding channels is recommended by many.
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As far as traffic is concerned, the busiest snarled corridors during the weekdays tend to be :
-Rush hour mornings to Anchorage (inbound) and early evenings leaving Anchorage (outbound) on the Glenn Highway could involve as bad as gridlock when a traffic accident or wildlife encounter happens....there are so many kamakaze drivers in a hurry to get to work between Wasilla and Anchorage in the morning that in my opinion from 530am to 900am timeframe is the most dangerous commute on that highway in the one direction.
-Tudor Road between 200pm thru 600pm.
-Old Seward Hwy. between 400pm and 700pm along Tudor Rd, International Bl, and Dimond Bl surrounding intersections.
-Lake Otis Pkwy between Northern Lights Bl and Dowling Rd during rush hour morning and evening can get snarled at times too, however the worst intersection as far as traffic movement is concerned is the Lake Otis Pkwy and Tudor Rd intersection, as I learned a long time ago not to go near this intersection on a weekday until after 900pm if commuting thru there, or spend some time waiting 15 to 30 minutes to pass thru between 600am thru 800pm.
-Downtown traffic isn't all that bad as it seems to flow ok most of the time during peak traffic.
If (but highly recommending 'when') planning for a drive to or towards the Kenai Peninsula on the Seward Highway, Friday afternoons seems to be the busiest time for traffic when leaving Anchorage in that direction while more kamakazes appear on that day of the week on the Seward Hwy more than any other time.
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With all the many recommended places mentioned by everyone within Anchorage and the outskirts, you will not be able to see them all in 4 days anyway.
Trackrig posted the many links well worth mentioning and seeing, as well as Loggenrock and Joe both mentioning the Alaska Native Cultural Center and Hatcher Pass-Independence Mine State Park outside the Palmer area which I also highly recommend, if you do plan on heading to Hatcher Pass you might as well stop at the Musk Ox Farm that is somewhat nearby which I visited in the mid 1980's.
The Alaska Wildlife Conservation Center is near the Portage-Whittier turnoff as I took my Mom there once, in Seward the Sealife Center and Exit Glacier are the main attractions, as I only been to Exit Glacier but havent seen the Sealife Center, as they have fjord tours in Seward as well.
Surprised no one mentioned driving to Flattop Mountain (Chugach State Park along east side of Anchorage) having a great birds eye view of Cook Inlet, the Anchorage Bowl, Fire Island, with a distant Mt. McKinley (Denali) on a clear day.
Perhaps if you end up in the immediate area, a quick visit at the Alaska Railroad headquarters at Ship Creek (where the A street bridge-Port of Anchorage-Government Hill and Downtown all tend to meet), while watching people catch salmon (or perhaps fishing for them) and taking a stroll along the coastal trail which is worth an hour or so to check out, quite an easy access and not a real congested area either.....Alaska Railroad has a gift shop as well as the Alaska Ulu factory within a few hundred footsteps, and if timed right there would be a flea market going on nearby as well.
As I agree with Joe that Earthquake Park used to be a nicer place (even upon my era), for whatever reasons it is not the nicer park it used to be due to youth nature leaving trash and not cleaning up after their bonfire parties at times, however just west of Earthquake Park (which is the west end of Northern Lights Bl) is a nice spot with parking access called Point Woronzof (north end of the Int'l Airport) where both Cook Inlet and Knik Arm start that is worth the view to visit, while viewing Mt. Susitna across the inlet.....Postmark Dr is a great shortcut thru the airport to get to or leaving these two areas mentioned with quicker access to midtown or South Anchorage, as you bypass the heavier traffic on Northern Lights Bl during the peak hours in the West Anchorage area.
Every other city park in Anchorage (and there are many of them) are real nice and well maintained, even the handful of dog parks are well maintained.
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Since grub was mentioned, there are many places that are the bomb and some average and not so average....
My favorite place for pizza is Moose's Tooth bar none, Mafia Mikes was good too but I don't think they are around anymore.
Although Joe mentioned the popular Arctic Roadrunner, I never eaten there but I did eat at the Peanut Farm across the street during Fur Rondy 2004 with a great atmosphere....my favorite places in Anchorage for a great burger was this irish pub restaurant inside the Dimond Mall but can't remember the name, Red Robin produces great burgers too, I don't know if Koot's still serve a lunch menu these days but the world famous Chilkoot Charlies bar sure served a great burger with fixins that really filled your stomach at a great price for under $5 during lunch hours as I was more than impressed.
Oriental restaurants seem like the slight majority in Anchorage as my favorite two places in this catagory are the Chinese Kitchen (a real hole in the wall place) and Twin Dragon, but there are so many great oriental places to eat as far as Anchorage is concerned.
As me being more of a chinese food toad and a mexican food toad when dining out, my favorite Anchorage places for mexican food is any Gallo's owned joint (which includes Taco King and Burrito House locations), and La Mex is my other favorite as well...Out of all my times in Anchorage dining at mexican food places, the only one mexican restaurant I visited that was not owned by Gallos or La Mex I ended up with a case of food poisoning.
Lots of fine dining in Anchorage although I never had the desire to spend big bucks with all the other great places to eat at, the Hilton and Captain Cook do come to mind with a great view while dining, I imagine the Marriott and maybe the Sharaton will have some form of upper level restaurant, as Anchorage has Benihana and those fine dining types as well.
Cant comment on any seafood places as I cannot fathom it.
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Now that Mr. Whitekeys was mentioned, I got the chance to meet him briefly a while back as he is friends with a couple friends of mine who were raised a half mile from my residence, the one friend was also an entertainer in Anchorage now residing in the Seattle area, who used to also appear on the former local music cable channel catch 22 in Anchorage.
I finally seen Mr. Whitekeys' great show at the old Fly By Night Club at another time, the show was real fun and entertaining and is based on comedy, musical, and skits of current and past people upon events non other than : Alaska !
I also really liked the segment when people fill out cards describing their celebrity encounters.
Mr. Whitekeys also has a book published called Alaska Bizarre that I purchased which tells some wild true stories that took place in Alaska, famous politicians and celebrities pertaining to Alaska, with a little insight of certain skits explaining why it's presented on his show, and other unbelievable Alaska bizarre stuff in between.
This year his show will reappear from June 17 thru August 21 only three times per week as it is been a limited returning event the past couple years, after officially calling it quits over a 25 year span back in 2006 or so.
If arriving in mid June or later, I would also highly recommend the Whale Fat Follies show.
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I driven 58 round trips to Anchorage and back (14 of those trips were'nt leasure trips as transporting my Mom on health issues) as I still feel I havent been in Anchorage long enough (my last visit in 2007), despite the typical problems Joe has mentioned about Anchorage (as I feel the exact same way towards Fairbanks), Anchorage is still one great city in my opinion but over 99 percent of crime that happens in Alaska the typical tourist never sees it.
I have always wanted to live in the Anchorage area since day 1 I stepped foot on Alaska soil, however it would be a major step backwards for me if I were to ever do so.
Wherever the OP chooses to see and do while in Anchorage and vicinity, you can't really go wrong on deciding what.
