My wife and I just got back from Jackson Hole 2 days ago after spending a week there. We absolutely loved it. The trip was originally scheduled around a friend's 40th birthday, and we decided to head up there a few days early and make a vacation out of it. We felt weird not going up to Yellowstone, but decided there was plenty in and around JH to occupy us this go-around, so we saved Yellowstone for next time.
A few highlights for us:
* Hiking from the Jenny Lake boat launch on the south bank up to Hidden Falls on the west bank and taking the boat back across. We did this on our last day there, and it was a nice easy hike to end the trip on for us. We don't have any kids, but this hike is easy enough for kids regardless of age as long as they can walk. The falls are awesome.
* The Park Rangers won't give you any details since it's "off trail", but we hiked up to Delta Lake on our 2nd day in town, and we couldn't stop talking about it for the rest of our trip. It's a bit NW of Bradley Lake just off the trails for Surprise & Amphitheater Lakes. Although enough people know about this lake at this point, so there is a discernible "trail", it is still very much a difficult hike at points. Definitely not for kids or anyone unsure of their footing/trail ability as you can definitely hurt yourself pretty easily with one slip. And I wouldn't go alone. If your kids are young enough to be with you the entire time, then I would rule this hike out. However, if you and the wife are up for it, the payoff is incredible. The lake sits in a valley at the base of the Grand Teton peak, and the view is absolutely unreal. Just google "Delta Lake."
* The fishing won't be all that good for another month or more, but if you enjoy fly-fishing, it's worth the time to throw a line into the Snake River or one of the many lakes/streams inside Teton National Park.
* It sounds weird, but it's hot enough right now that the alcoholic frozen drinks that they call "sloshies" around town hit the spot. I can't even recount how many I consumed last week. Our fav is at the Creekside Market on Cache St. just north of downtown. "The Hound"...essentially just a frozen greyhound cocktail.
* Million Dollar Cowboy Bar. Not necessarily kid friendly, but it's worth your time to stop in and take a look. The bar seats are horse saddles, which I imagine the kids will get a kick out of. Even Kanye had to sit in one of the seats recently while he was in town. I spent most of the next day hungover after we met some strangers at dinner the night before and ending up playing pool here until God knows what time.
* Local Restaurant & Bar. Great burger.
* Snake River Brewing. Surprisingly great food for a brewery.
* Persephone Bakery. This place is fantastic. Great spot to grab a seat outside on their patio and enjoy a really good breakfast and coffee. And I think there is a toy store across the street if I remember correctly.
* There are a number of Thai places...4 or 5, I believe. We went to Teton Tiger for lunch one day and loved it. We heard good things about Teton Thai as well.
* If you're in JH on Tuesday, go to the visitor center just north of downtown on Cache St. for "Talon Tuesday." There is a bird rescue organization in town that does educational presentations that your kids would probably enjoy. We didn't see them at the visitor center, but we did see them at Amangani on Friday night and it was fascinating. Btw, Amangani. WOW. It's like $1k/night to stay there, but they'll let you drop in for drinks and food. The view is amazing.
* Take the gondola up to the restaurant in Teton Village. Incredible view, and the kids should enjoy it.
* Dornan's Chuckwagon on the Snake River just outside the Teton National Park visitor center. This is a really cool place. It's the kind of breakfast and coffee situation that you would expect from a chuckwagon. We weren't expecting it, but this was something we really enjoyed.
* Not sure if your kids are old enough, but we went horseback riding just on the outside of Teton Village and enjoyed it.
There's so much else to do that I wouldn't stress about making a strict plan that you feel you have to stick to...it's such an incredible place that I really think you'll have a blast regardless of what you decide to do. We didn't have much of a plan for our first 3-4 days there, and this was honestly one of the best vacations we've ever taken.
Have a blast!