In reality, for human powered effort, a splitboard is the way to go. It opens up 10x the terrain you can access by boot packing and snow shoeing.
Still there are places that offer pretty good riding for the boot packer/snowshoeing rider.
Teton Pass is an obvious first choice. From my general understanding of the area, is that a good number of the roadside attractions, there is no better way to access the goods than by just postholing it. There are longer tours where a splitboard would be the way to go, but there is generally a set boot pack on most routes unless you are the first. As far as where to stay around Teton Pass, I'd check with the Hostel in Jackson and look at Driggs Idaho on the other side of the pass. I do not know the winter camping situation around there. I do know parking at the top of the pass is problematic and I doubt the forest service allows for vehicles to be there overnight. Expect to park down low on the pass and hitch hike to the top frequently.
Berthoud Pass in Colorado is the best spot in Colorado for the boot packer. There is generally two boot pack trails on the East side and one on the West side. All three allow you to access all of the old ski area runs from the top of the pass. There is a warming hut at the top of the pass with restrooms. Pit style and not always pretty. The hut does have radiant heat floors though and is a great place to eat lunch, change out your gear, and have a beer at the end of a great day. No overnights in the hut though. I do believe you can leave a car parked at the top of the pass though.
There is the Peter Rabbit hut on the North side of the pass. It's up the Current Creek drainage about a quarter mile. It's a pretty easy hike and the hut is first come first serve. It's not maintained by any organization, and I will say that the wood stove there is getting close to be a "hippie killer". It's getting sketch. The hut sleeps six I believe. Weekends are when it's the most popular, during the week not so much.
Grand county huts is opening the Broome hut in Second Creek on the pass this season. It looks to be awfully nice and is a relatively easy snowshoe in. I think their prices are around $20 a night, not sure on availability. The terrain surrounding the hut is so so. I certainly will not lap it. The good looking stuff up high is also deadly. Two people got banged up last season making bad choices to go up there when the avalanche conditions were sketchy to say the least. They did get to keep their lives, but received lots of broken bones for their efforts. Generally speaking that is not a spot you want to tangle with until late spring.
There is also a hut near the top of the pass on west side. It's off a run called the Plunge through an area called the 90's. It's a small little hut just off to the right of Plunge in the trees when you hit tree line. No stove, but lots of candles and a platform to sleep on.
I am assuming you have taken an avalanche course and have the requisite gear. The snow pack in Colorado, Wyoming, and Utah are the most dangerous anywhere in the US. Colorado in particular leads the nation in recreational avalanche deaths. Good decision making skills are a must. Even if you are not familiar with a continental snow pack, sticking the basic tenants of a Level I course will serve you just fine. That knowledge should serve to keep you from putting yourself in a dangerous spot.