Clean and comfortable Hotels close by?

Yes, there are several good places in the area. If you use Google Maps you will be able to find places that are close.

Yes there are a few good hotels that work with Moffitt and have shuttle services to and from. The Marriott is one of those hotels but im sure Moffitt has a list if you call them or check their website.

I would assume the hospital has a list. I don't recall seeing any. Mostly college campus.. Perhaps Google it,?

Really not to sure