When I went I stayed downtown at the double tree. It was a great hotel. If you call the hotel I think you can get a discounted rate of only like $89/night or something like that. You can stay downtown where there is a lot of stuff to do and it's a quick walk to the rock and roll hall of fame. I also took the shuttle to a Cavs game.
The shuttle also goes up to Case, but you might have to take a cab to campus, because the shuttle only goes up to Case at either 8am or 10am, so it kinda is at awkward times since I think it's 9am when you're supposed to show up. It was only like ~$16 to take the cab up there, and then I took the free hotel shuttle on the way back.
I suggest taking the public transit in Cleveland if you're staying at a hotel downtown. It's dirt cheap to take the train into public square and then you can either walk or take another trolly (free) to the hotel. Public transportation in Cleveland is great.
Enjoy Cleveland and Case. I got into Case and I loved the school, but I got into my state school so it was a no brainer decision for me. You will have an interview with two people lasting an hour each. It's very relaxed and conversational.
Good Luck!