Two top has lots of trail and lots of meadows right alongside the trail. You will need both Montana and Idaho stickers though (if you're renting you won't have to worry about stickers). You can also ride to Island park from there if you want to.
I've done Horse Butte before with some very young kids, with the new snow we've had the last few days that could be a good ride for beginners looking to try a few pow turns. There are some good open meadows along that trail too, just stay off the lake.
Pick up a trail map at a rental shop or dealer in town. There are usually good trail recommendations in there as well.
Anything that's easy to get to will probably be busy, but I've noticed a lot of tourists start late so the earlier you head out, the better. We usually leave around 8 and try to get back to the truck around 3 or 4, and it's not uncommon to run into people just heading up the trail as we're headed down.