marlin said:
I plan on doing a 2 day hike. No car for me. Just gotta find a good spot, say a 15-20 mile round trip on foot. I will probably end up winging it and just finding something that looks interesting. Depends if anyone else wants to tag along. Snow should be no problem, I have cold weather gear, just means I am in for some cold nights. Its the mornings that suck, awfully hard to get out of the bag when its 20 degrees outside and you have to break camp :shock:
If I can make one recommendation my all time favorite Yellowstone trip is Bechler Canyon, best trip ever if you like waterfalls. It's in the SW corner of the park, trailhead is at the Bechler ranger station.
If you have 2 nights you could do Bechler Ranger station up to a campsite on the river in the canyon (you have to stay at designated campsites in Yellowstone). From there you can check out some of the waterfalls in the canyon like Iris Falls, and Colonnade Falls. The next day you could head back down the canyon, and through the meadows to a campsite that is right by Dunanda Falls.
Dunanda falls has a hot spring right at the base of it. So you can sit there in the river at the bottom of the falls in 100° water just like a hot tub, with the ice cold river dumping on top of you.
It's awesome!!
Then around the other side of the meadows back to the ranger station. With 1 night it might be difficult to pull off, maybe just Dunanda falls and back, depends how far your willing to hike in a day.
Some pics from my last trip there.
Colonnade Falls
Iris Falls
Dunanda Falls
Anyway, don't let me influence you.

Wherever you decide to go, you
DO have to plan ahead. Since you
HAVE TO reserve campsites, and pay the $20 entrance fee wherever you go, and listen to the Rangers little 20 minute safety spiel. I think I heard that they now require bearspray too, not sure.
Another fun trip I've done is from Old Faithful, down to the north side of Shoshone Lake, up to the other end of the lake and back. There are some really neat thermal features around the lake, and if you fish you won't find anyplace better.
Sorry I don't have any pics of that trip online at the moment.