I'm gonna be at YSNP and GTNP in a couple of weeks. What were you favorite things to see?
We did the standard loop in GTNP and it's pretty great as far as a nice scenic drive with lots of opportunity to see wildlife (elk, pronghorn, black bear, grizzlies and bison although we did not see any bison or grizzlies). We hiked with the kiddo in a pack around string lake which is between jenny lake and leigh lake and it was about 3.5 miles and really nice if you're seeking a shorter hike. Would have loved to have gotten up into the trails on the west side of jenny lake or jackson lake but with the kiddo an 8+ mile adventure was not in the cards.
If you fly fish, there's a ton of opportunity in both parks and I have also spent some time on the south fork of the snake outside Victor, ID over teton pass which is a fantastic place to book a guided trip if you're interested in that sort of thing. We camped just outside GTNP at gros venture campground and it was a greta location. Also can walk from the campground to the gros venture river and do some fishing. I immediately encountered a deer carcass on my walk to the river which was a bit unnerving but I had bear spray with me and tried to whistle and make a bunch of noise as I romped around. I actually found a recommendation on this site for a dirt road within the park that has since been washed out by the snake river - you can still drive out a portion of the road to an old dude ranch and it was really cool - the views are spectacular and we drove right up to a moose down there which was pretty neat. The road is on the east side of hte GT loop road about .a quarter mile north of the taggart lake trailhead (I believe it is called cottonwood creek road but is unmarked). Worth driving out there and back, doesn't take too long.
Yellowstone we had reservations at the bridge bay campground (showed up to that really large elk in my photos basically hanging out at our campsite - I understand that bison and bears often frequent the campground as well - you can purchase bear spray throughout the park) and did the lower loop which took us by old faithful, the grand prismatic, firehole loop road, the grand canyon of the Yellowstone (we went out to artists point with about 1,000 Chinese tourists) - all of those things were great to see. You'll probably see a ton of bison in Hayden Valley there as well.
I really enjoyed the drive out through Lamar Valley in the NE corner of the park - we've tried getting their at dawn a few years back and hit an elk in the dark outside the park near Livingston, MT totaling our car (so drive safe at night lol) which ended that plan, and with the kiddo we couldn't make the timing work until a bit later in the day, but morning and evening you're more likely to see wildlife when they're more active - there's grizzlies and wolves (and elk, bison etc) out there although both are pretty elusive. THat area of the park would be a great place to do some backcountry hiking and backpacking if you're into that sort of thing but I imagine permits are very competitive to get if they're anything like the other big NP's so I'd call the NP office ASAP. Thus far between approx 20 days across yellowstone/teton/glacier national parks I've encountered 1 grizzly and it was 10 miles deep into the backcountry (I'd much rather encounter one from the comfort of my vehicle lol) so hopefully you'll have better luck spotting some!
Honestly, I really enjoyed both parks but I found some of the driving through Yellowstone less enjoyable - lots of really thick forest that after awhile is a bit of a bore. Otherwise the scenery and terrain are fantastic. We exited the park out the NE entrance into Montana before taking 296 south towards Cody, WY and frankly that part of the drive was my favorite - absolutely beautiful and some day I'll back and drive the rest of the Beartooth Highway towards Billings.
Don't forget to bring a good pair of binoculars! Also you'll have zero cell service throughout YS, so be prepared for that. I told my office I'd have intermittent service and then went dark on everyone for 5 days lol.