From GA to the mountains in CO is 2 1/2 days for me easy, every time. From CT since you are a little further East already then 3 to WY. i-80 from the river west seems like it is all uphill, and very rough road.
Depends how long you drive each day. Mapquest.com will plot out your route and give you driving time. Add in stops to make a complete day.
I would go into WY and thats Yellowstone land, then into UT make a stop in SLC to see the salt flats if you like that, stop and swim in the lake if you have never floated in that much salt - Antelope Island has parking and beach showers. Then head east to Arches NP in Moab, UT. You can go south and there are many worthy NPs inclding Zion, but it will be hot hot in the summer. Anything under 95 degrees is not hot. Over 100 is hot since it is 10% humidity, not like the 90% humidity you are used to in CT.
Then into CO. Take the Million Dollar Highway drive if you can, that will drop you eventually to Grand Junction CO at i-70 then you can tour the high mountains where all the ski areas are. Ski area in summer have ample RV parking and some will let you boondock overnight, or some have parking for a small fee.
You won't be far from the North Face of the Grand Canyon if you go to Zion, so that is worth the trip down, getting to the South rim is a huge drive, but the N side will give you a great view.
There are yearly / 12 month National Park passes for $80 or discount for seniors that will get you into all USA parks, so this might be worth it. Not all NPs sell these so plan ahead.
Part of the fun for an East-coaster person is just parking for a few days in a spot and soaking in the beauty of such a different place. dont be in a rush to get to the next spot. I like seeing fewer spots spending more time in one spot rather than seeing a bunch of spots Griswald-style.
Happy Camping