Shenandoah National Park (not tri related)

For waterfalls I'd do the White Oak Canyon/Cedar Run loop. Another "mandatory" hike in SNP is Old Rag, a quite difficult but fun climb with some rock scramble involved. Little Devil Steps/Big Devil Steps are also some good hikes, and if you have time check out Thorton Gap, a lung buster of a climb to one of the best views in the park. Most of the good stuff is in the mid-to-north sections of the park, so whether camping or lodging, I'd recommend Big Meadow, Elkwallow, or Skyland. If you aren't interested in staying in the park, I won't be much help, but maybe theres someplace in Luray or Front Royal where you can stay. Let me know if you have any further specific questions. I've hiked most of the AT through SNP and stayed at several of the Backcountry cabins, so if you are interested in back packing, I might be able to point you towards a 4-5 day loop you can do.

Another option I just recalled are the PATC cabins which are back country but require prior arangements to access. Just look up the Potomatac Appalachian Trail Club.

Luray has some interesting caverns as well, if that interests you at all. Wine tours/tastings are available to both the east and west of the park, for some added value.

You might get some snow that time of year, but I don't think it should affect the road much. The only time I've seen the road shut down for extended period is in the February/March time frame. They do an awesome Turkey Day Dinner at Skyland, if you're coming around that time.

I don't have much to recommend for that type of lodging, outside of the park. It may be tough to find, being off season. But like I said, check in, or around, the towns of Luray and Front Royal. Maybe something Sperryville might have something to offer as well, it's near the base of Old Rag. I'd dare say you'd probably have better luck with some of the cabins inside the park though, like those at Skyland or Big Meadow. The prices should be reasonable, off season.

Good luck, and have fun... I may ask you the same questions someday about the mountains in NC,

To stay near the park, google Lydia Mountain cabins. They're near Stanardsville, Va, toward the middle of the park.PM me if you have trouble finding them.I stayed there and it was very nice!

I can see Old Rag from my back deck, so I'm not sure what to tell you about lodging... but White Oak Canyon and Old Rag are great hikes.  

SNP is my backyard I totally agree that White Oak canyon is a must, also Stoney Man. Also be sure to hit some of the local vineyards. There are literally dozens of vineyards and wineries within 1 hour of the southern terminus in Waynesboro, VA. Just take I-64 or VA-250 east and follow the signs with the grapes.