We have done Yellowstone and Grand Tetons twice in the last 3 years. First time we gave ourselves 5 days for Yellowstone and knew we had to come back before we left.
RV campgrounds - Just one or rotate, likes, dislikes
We stayed in Gardiner the first year and West Yellowstone the 2nd year. Gardiner felt further away and the RV park was too tight for our liking so we tried West Ystone and liked it much more. We stayed at Grizzly RV Park. It was very nice, think it's newer. Very kid friendly (we have kids) with all the amenities. Stay on the south and west side of park, which is away from most commotion and right next to park land. Take a look at a satellite view on google maps. We would stay here again. We looked at fishing bridge, smaller RVs are better and it seemed further away from most of the the things we wanted to do. And unless you cook all your food or just love national park food, it's not an easy drive to get something to eat or pick up a few things at the grocery store.
Getting around with/without a car
We had a car. Lot's of people driving around and parking with their Class Cs. The later you go the more packed it will get and it will be harder to park. Remember, Yellowstone is huge. Plan for appropriate drive times in the park (these are not 4 lane hways), which include other slooooow RVers, tour buses, the parks classic tour cars and don't forget wildlife. Traffic is much lighter in the morning, but wildlife sitings will slow things down and the main reason for a traffic jam is buffalo on the road who don't want to move. This is not uncommond on the east side of the grand loop. The drive from Yellowstone to Grand Tetons has a couple of passes to go through, but wasn't a problem in our Class A.
If only 7 days top 5-7 things to see
Number one stop is visitor center. Then you have to know what you like to see. If you like Wildlife like buffalo herds, bears and perhaps a wolf (eventually elk are a dime a dozen) then an early morning drive to Lamar Valley is a must. Unfortunately there are no guarantees but we have been lucky and we have struck out on the wolves. If you want to see the features and can stand the incessant sulfer smell then the Grand Loop Rd between West Entrance Rd and Old Faithful has multiple stops and features culminating with Old Faithful. If scenery is your thing then the East side to the Grand Canyon and the Falls are awesome. On a 5 day trip you can do all these and a few more. Those would be my top 3 followed by Mammoth Springs, and maybe some evening fly fishing on the Yellowstone River. Lake Yellowstone is huge and pretty, but we weren't going out on the lake so only spent a couple hours in the area. Fishing bridge is just and old bridge over the river. People in the past overfished the native cutthroat so you don't even see any fish.
In Grand Tetons we have stayed at Colter Bay twice and would do it again. Love the Tetons. Last year we took the boat across Jenny Lake and the hike on the other side. The hike was very steep for the first part then much more enjoyable the final 3/4ths of the way.
Cell and hotspot reception?
No problems with AT&T outside the park, but don't expect much when you get into the park.
Bonus Extra: we got up early drove the Lamar Valley, out NE entrance rd (saw 3 grizzlies, pack of wolves and tons bison), stop in Silvergate Montana for a hot breakfast then a drive up the Beartooth highway and back. Very pretty drive if you like mountains, but easier done in a car and not an RV. I wouldn't take my class A.
Good Luck and have fun!