LaQuinta @ Cocoa Beach was severly damaged by the hurricane late last Summer. When we were at Port Canaveral in Nov., it was closed and did not appear to be under renovation, but that may have changed. Many A1A hotels in the same area were hit hard: Hilton, Courtyard, Holiday Inn. Radison was the best bet and nicest property. We stayed at the Best Western and I do not recommend it.
Yes the LaQuinta Inn Cocoa Beach is open and is very nice. My DH and I stayed there before our December 12th cruise. I don't know if they have shuttle service. We had a car with us and drove ourselves to the port. They are not on the beach but are across the street within walking distance of the beach. They were very friendly and helpful at the front desk. Also, the continental breakfast was delightful. Muffins, yogurt, fruit, make your own waffles, coffee, juice and cereal. The pool at the hotel was very nice also.