I just drove myself through Teton and Yellowstone from June 2-11 of this year, so here is my updated review/advice/thoughts:

Unless you are specifically in Teton for sunrise or sunset photos at specific spots, I think you can do Teton in 2 full days, 1 overnight in the area. I recommend coming in from the north, following the inner loop for the views on the way in and to get to most of the hikes and lakes. Maybe continue that way and do Teton Village that evening, ride the tram, go visit Jackson Hole, sleep, the come back north around the outer loop and the majestic views you can get there on the second day. Moulton's Barn, Schwabacher, and Snake River Overlook are all on the outer loop. Seriously, the views are there at all hours and like I said, if you are not specifically wanting to be at a place for a sunrise shot, the view at any time is amazing. Check out the view from the Jackson Lake Lodge as the sun sets, eat a hearty meal, stay there or continue north. I found cell service almost everywhere. Not the fastest but at least it was there. I am on T-Mobile for reference.

Yellowstone is much bigger with everything more spread out. I was alone with no spotters so I didn't see any wolves or bears while drving around, but found most of the internet advice to be sound. The Lamar and the Hayden valleys had bison everywhere. Like after 1 day I wondered why anyone ever stopped for bison because they were everywhere! Anyway, I'm not sure I can give a recommended plan of attack here because I didn't actually go everywhere. There are more hike options and less scenic pull-outs. I did not visit the lake area really at all. I did drive up that way through Hayden Valley to Canyon Village. Canyon Village was nice, the Lodge and area were nice. It is very close to the north and south rims of the Canyon. There is some road work being done there, single lane traffic along part of the loop and part of Uncle Tom's trail is closed. Artist's Point is open as usual and the rainbow on the lower falls appeared right around 10:00. If you continue up to Tower Junction, there is not much other than Mt. Washburn on the way. I stayed at Roosevelt for 1 night and thought there was not much up there. However, this is a good base if you want to head out the Lamar Valley the next morning to go wolf and wildlife spotting at dawn. Further along to Mammoth Hot Springs area where there are of course the hot springs plus Yellowstone Fort and a couple of restaurants. I'd say drive past, start at the top of the springs and walk down the viewing platforms, eat lunch, visit the Fort and Village, then walk back up the road or the viewing path again, but that is just me. From Mammoth to Norris Geyser Basin, the Earth is on fire. There is stuff bubbling, steams, or shooting up almost everywhere. Enjoy. Norris Canyon Rd. is scenic and cuts back to Canyon Village. Otherwise continue around to Madison Junction. Not much there except the road out the west entrance to West Yellowstone (if you need internet access or different food options than the park offers) or continue along the loop to the Firehole River side road. Follow that. You actually have to pass it then turn left since it is one-way. But that was a nice side show. Get back on the main loop and visit the Paint Pots or continue south to Grand Prismatic. There used to be a walking path to Fairy Falls which is an overlook for Grand Prismatic. it is CLOSED! Scheduled to open in July, but the ranger I talked to said he expected September 1st at the earliest it would re-open. Lame. However, do not miss Grand Prismatic. the parking there sucks so get there early or after dinner, but even though the view is not overhead and sweeping, it is a very impressive site. After that, continue south to Old Faithful. It has its own exit off the loop road, it has plenty of parking, several places to eat, several geysers to view (I was lucky enough to see the Beehive Geyser shoot 200 ft into the air and douse everyone on the boardwalk), and the Inn and Visitor's Center are great here. Old Faithful lived up to its name while I was there, every 90-95 minutes it erupted. It is very entertaining to see the masses of people there for the show and then 10 minutes afterwards, 3 people on the benches. Anyway, you could spend anywhere from the full 90 minutes to several hours here if you wanted. Continue widdershins or east to the Yellowstone Lake and you are back to the road leading to the south entrance. There is little to no cell service in the park. I would randomly get an email through at an unnamed geyser, but that was about it. You will be stopped for bison. probably more than once. It's like they do not know to stay out of the streets...and even if they did, the cars would stop to view. No complaints, just a warning. If you want to be parked close to a major attraction, be there before 10:00 or after 19:00ish. Everyone is out between those time. The first week in June was not actually super crowded. I did not feel crushed, the few hikes I did were not populated. I'm sure that will change in a week or 2. For comparison, I got to Artist's Point at the Lower Falls at 9:30 the first day, no parking. I got there at 7:00 on another day, there were 3 cars plus mine and a coyote in the parking lot. Big difference.

Anyway, hope all that helps. It is at least recent. Eventually I will have the pictures off my camera and I will link them for reference. Until then, use you imagination