Another great place with fantastic trails is Togwotee.
You can stay in Debois (cheap) and trailer up 10 minutes or so to Tie Hack parking area and ride from there.
They groom the trails literallly every night.
it's also about 6 hours closer than West Yellowstone or Island Park.
Link to trail system.
Here is a map of West Yellowstone/Island Park trails. They are connected.
There is a big plus to riding from West Yellowstone.
You can ride from where ever you stay and don't have to trailer anywhere.
There is lots to do each night after riding.
If you want to take a day off you can hit the Grizzly/wolf habitat and see the critters.
You can spend around 120 each and take a snowcoach into the park or spend 200 each and take a sled in.