A lot of the campgrounds don't really even 'open' in the Hills until May or so... You could probably find one with some searching. I havn't been out in the hills much before May (at least not camping), so I'm not 100% sure...
I've stayed at the Days Inn in Custer before - it was pretty nice... Just did a quick search for mid April and it was like $40 - 50 a night....
Shoot a lot of campgrounds with decent facilities are 15-20 - so it may be worth the extra bucks to know you aren't going to get snowed on...
Good luck!