I've got an opportunity to disappear off the face of the earth for 4 days, and I'm looking for a place in Colorado (can be anywhere not just front range) to set up base camp that will provide good access to relatively easy alpine climbing. Steep Snow Couloirs, AI2-3, or M2-4 will do. Plan is to hike in on day one and climb for the next three.
The Long's Peak Cirque might have what you are looking for (Lamb's Slide, Martha Couloir, Dreamweaver, Kiener's). The problem is, you can't set up a tent. It's bivy only. There are some great caves though under some boulders. The best are on the west side of Chasm Lake, which will put you farther from your objectives. You will need to get a bivy permit from the ranger station. You could spend day one getting your bivy permit, hiking in and finding a home sweet cave.
Another more remote option would be Lone Eagle Cirque. I haven't been over there in the winter but there seem to be a lot of cool options for snow climbs (and ski descents!). You can also set up a tent at Crater Lake. It'll probably take you a day in and a day out from the east, but the hike would probably be a lot easier from the west. You will definitely be more isolated!