Oh, I was just there in January! You lucky dog...take me with you! I can guide you around the mountain!
It depends on how much you want to spend:
1) The Four Seasons just opened last season, brand new, ski-in/ski-out, absolutely gorgeous but pricey. Not a Western lodge feel, everything is darker wood, cherry or something like that. If you have kids, 18 and younger stay free in parents' room; discounted if in separate room. There's a teen center, health club, outdoor pool, hot tubs, etc. Rooms have fireplaces. OK, hate to say this, but not the best meal in Jackson...they have a lot of very worthy competition. A bit of an attitude here too.
2) Snake River Lodge & Spa, another upscale place that's lovely. Rich colors, but not dark, like creams and beiges. Some rooms have fireplaces and jetted tubs.
All rooms have fridges and coffeemakers, granite baths. Sizes range from standard room to 2- and 3-bedroom suites. If you have a wife/girlfriend who likes spas, stay here. There's a pool and hot tub. You'll pay top dollar here too.
3) Extreme skier Rob DesLauriers just opened the Teton Mountain Lodge, very swanky condo-hotel. Elegant Western mountain lodge feel to it; full-service. Custom kitchens, stone fireplaces, dark rich colors, woodwork, overstuffed leather chairs. Again, it has in-room jetted tubs.
Spa services too. Restaurant is very good. Pay top dollar here.
4) Alpenhof Lodge is one of the original slopeside lodges, classic Bavarian style, outdoor pool and hot tub, with an excellent restaurant. If you're into staying at a place with history, this is a great choice. More leeway in the price range here, but can still be pricey.
5) Stay away from Best Western Inn at Jackson Hole, it was renovated but still looks old; also all hotel rooms open onto outdoor walkway. BRRRR. And sound proofing? Forget about it!
But they have very good restaurants there.
6) There are a slew of condos. Some are ski-in but you have to walk to the lifts; some are ski-in/ski-out. If you call Jackson Hole Resort Lodging, they can hook you up with what you want. We stayed in Windriver, very nice, but had to walk to lift (didn't bother us, might bother you).
7) OK, this one is not slopeside, but I'm going to mention it anyway because it's an awesome place: Spring Creek Ranch. Understated elegance with a Western flair. Despite the seclusion and wealth of amenities, it’s not stuffy or pretentious. Awesome views. Has a spa and Nordic center. Free airport, town and ski shuttles. Deluxe rooms and condos; hotel rates include breakfast. Food is fabulous, definitely one of the top places in Jackson. Pricey but completely worth it.
I've been inside all of these. If you have questions about any of them, I can probably tell you more. I can also suggest some more places to eat.