If you want space for your rig, Grizzly RV is the place. There are a few sites with no hookups inside the park where you'll fit (Bridge Bay CG comes to mind) but the only CG inside the park with any hookups whatsoever is Fishing Bridge. Agree with Jim Shoe that it's tight in there. I've seen bigger rigs in there, but have no idea how they got into their sites. We had a devil of a time backing our 27-foot TT into ours.
Grizzly RV is close to the west entrance, not even 1/2 mile I think, and the drive along the Madison River from the west entrance to the Grand Loop Road is plenty scenic, lots of wildlife viewing opportunities (especially in the evening). It can get backed up at that gate, but that's life in/around YNP.
Teddy Roosevelt is good (remember, it's dry camping in the park). I second the recommendation for Little Bighorn National Battlefield. There are self-drive tours or van tours of the park, and a ranger presentation every hour, which are all different - it's worth spending at least half a day there.
Jamestown ND has the biggest buffalo in the world (a statue, that is) but there's a neat museum there with some area history, and a white buffalo on the grounds (live). Kind of a fun stop for a few hours.
One other thing to think about - if you have a microwave with a rotating turn table be sure to take that turn table out and store it securely somewhere. We've had ours pop out probably because of all the bouncing around on some rough highways. Chipped the ceramic turn table. Oh well, lesson learned.
We have a glass turntable in the microwave, and we wrap it in a dish towel, and make sure it's securely "seated" in the grooves that hold it. That has worked well for years. Slightly more work than removing the 2 rolls of paper towels.
The 5er will be more comfortable for that length of a trip, but the TC will give you more options not only for routes but also campsites. Oregon has some very nice SPs which the 5er will fit well in, but you would find more flexibility with the TC. Just some things to consider.
Mid-May can be good. If the longrange forecast for this winter holds, it's likely the snow may be gone from the roads by then; if not, then late May/early June are good. April is too early for most facilities, including CGs, to be open, and there is no boondocking in the park, even if roads are open. Baby animals will probably not be seen much until late May. If the park is open, there are other tourists there, but the crowds don't really start in earnest until mid- to late June, and get thickest from 4th of July through late August.
Definitely check on closing & opening dates for the various facilities online, as suggested, and keep up on it. Bear in mind that some of the larger CGs in the park are reservable a year or so in advance.
Congrats, and enjoy! You probably will end up with a different truck. We spent a good 6 years with our similarly-sized TT and a 1/2 ton. Still have the truck but downsized the TT last year. :) We also chose that big TT after a few years with a HTT.
Sounds like a great plan! x2 on Normandy Farms, but make sure to get a site in the regular part of the campground. The "Safari" area is cheek-to-jowl, no shade, like a parking lot on the grass. The regular section (most of the CG) is shady and pretty. Haven't ever been to Minuteman so I can't say how it compares. If you don't want to drive into Boston itself, you can drive from the CG to a suburban "T" (aka MBTA) station and take commuter rail into & around the city. (Fun fact: a "Charlie" ticket for the T also can cover the Boston water taxis - great for sightseeing!) Boston is one city I have never - and WILL never - drive in. Sorry, Bostonians, but as drivers, y'all are crazy. :)
As for planning the big western trip, I'd suggest using several different sources. The national park sites via nps.gov have "planning your trip" sections on them which can help with campgrounds, things to see, etc. I like your idea of spending 1-2 weeks in each national park area you visit! Most aren't lucky enough to have that kind of time. Consider staying in some national forest CGs near national parks - campsites may be slightly less expensive. Another site that I find very helpful is rvparkreviews.com. Great for choosing CGs that fit your needs, based on reviews by people who have actually stayed there. Others here may have other suggestions; I tend to use old-fashioned (paper) maps to plan our routes, and do the CG and sightseeing research from there.
The farthest-south CG in YNP that can accommodate RVs is Grant Village (no hookups); otherwise for the "south end" you would need to camp outside the park at Flagg Ranch (since renamed - not sure of the name of it now) or (better, IMO) Colter Bay RV Park in Grand Teton National Park. That makes for a long drive each day into the park. East entrance has a similar problem - a long drive into the heart of YNP from anywhere you can stay outside of it; the farthest-east CG inside YNP is Fishing Bridge (not "flying bridge"), which is an RV park, FHUs but very tight. Great for convenience but not for ambience, IMO.
The park is enormous - you'll spend an entire day just hitting the briefest of highlights for each of the two parts of the Grand Loop road in the park. Plan to spend several days in the park and base-camp in one or two spots. It will take you several hours to get between CGs because of traffic and wildlife (i.e. buffalo in the road, etc.), so plan accordingly. You could consider a base camp on the west or south sides (Colter Bay, Grant Village or Grizzly are good choices) for a few days and then on the north side (Mammoth - no hookups - or a private CG such as Rocky Mt RV Park in Gardiner, just outside the north entrance) for a few days, spending 1-3 days exploring each part of the Grand Loop. Another possibility is Fishing Bridge for your entire stay, since it's pretty centrally located - but again, no ambience, very tight sites. And should a car rental be needed, there are no rentals within the park - just in West Yellowstone, Gardiner, Jackson or Cody.
All entrances into the park except the northeast are RV-friendly, but some are more challenging than others. West entrance is by far the least mountainous driving, but all (N, S, E & W) are do-able. Just take it easy, and the driver may need to forego sightseeing in order to improve concentration on the road. :) People do drive through the park in big rigs with toads or trailers, but I don't recommend that except as a way to get to whatever CG you're planning to stay in. Otherwise, use your toad, tow vehicle or a rental car for the sightseeing.
Kit, you may get your wish if weather forecasts for the winter are true; the strong El Nino will bring a cooler, wetter winter to the southern tier, including the southeast.
Unfortunately we will continue to be warmer & drier than usual for the winter. It isn't common for Indiana to beat Idaho to freezing temps, but I guess that'll happen. Forecast lows for us for the foreseeable future are in the 40s, or maybe upper 30s. We winterized yesterday in 80-degree sunshine.