We stayed at the Sandman, when we went in May. You can leave your car for free for 7 days, if you stay the night. Or 14 of you stay on your return. We had two rooms so they gave us 14 nights for free. It's not a bad hotel, and they have a Moxies's attached. I think the shuttle was $15, I could be wrong about that though.
ETA: I just noticed that you were looking for secure parking. It's not secure at the Sandman either, but we had no problem, and I think the lots are patrolled.