Going to the black hills can be tricky. There is no time of the year where you are guaranteed good snow, especially if you want to take advantage of the offtrail opportunities. Going offtrail in the early part of the season can be risky as there is usually not enough snowpack to prevent hitting stumps and rocks, and the area tends to end early at the end of the season. Mid January to mid February seems to be the most reliable times, but you can't always count on that. We had to cancel a trip there that was scheduled for Feb 17 this year due to lack of snow. My advice would be to watch the snow conditions and not book too far in advance. Going in the middle of the week should make it easier to get last minute reservations.
As far as where to stay, Trailshead lodge is right in the middle of the trail system. Their cabins are nice enough, but they do not have kitchens at all. The lodge does have a restaurant/bar, but if you are looking for nightlife, a lot of people will stay in Deadwood or Lead. There are trails from there, but they are marginal or closed even more often, so some people will elect to stay there and trailer the 15 miles to Trailshead. They have a huge parking lot there and you can leave your sleds and trailer there overnight if you want. If you are looking to rent a house or cabin, there are quite a few in the Recreational Springs and Deer mountain area, but again, that is somewhat on the edge of the area, so you could still end up trailering if the snow conditions are not right.
I don't want to leave you with the impression that it is not a good destination. It is great there when the snow is good, The trail system is very scenic and they groom it every night. I believe they have 7 groomers for the 300 mile trail system. There are almost endless opportunities offtail with a lot of meadows, forest roads, and hills.