Are you talking free parking or paid parking ?
Parking in some of the downtown areas aren't much of an issue for free parking but can be a hit and miss depending what day of the week and what part of the day, but generally you can find a free parking space available or street spot.
Pay parking garages and pay parking lots are a non issue in the downtown area as they are plentiful (such as 6th avenue park and 5th avenue mall parking garages).
Although I haven't been in Anchorage in 9 years until last week's holiday weekend, I had not gone to the downtown area as I only spent 1 and a half days in Anchorage and yes I took the camper rig !....If I had wanted to roam downtown, (as far as a FREE parking spot goes, I would have found a parking street spot along 3rd Avenue near the A street bridge somewhere (east side of the intersection) or parked down in the Ship Creek area near Comfort Inn or near the railroad yard and walked around unless the area had significantly changed about the parking rules (I sure miss the place my friend's lived at on Government Hill as I always walked easily to downtown).....As there is always Diamond pay parking lots, across from the Alaska Railroad headquarters on 2nd Avenue and one up the hill on 3rd Avenue just west of the A street bridge near the Anchorage Hong Kong style looking Hilton.
As mentioned, the other side of downtown (south portion) has more opportunity for free street parking like the Delaney Park corridor (9th and 10th Streets).
We used the Walmart right on Seward Hwy, plenty of parking and Barnes and Noble is right next door for internet access
This particular area in reference is actually the "midtown" area of Anchorage and is not considered downtown.....as I noticed that the midtown Walmart here is no longer open 24 hours anymore.