Just an update since I posted this question... We decided to go with the familiar and stay at Cocoa Beach again. We got a good rate at the Doubletree, which has direct beach access. The hotel was good--the room was slightly worn, but the lobby, hallways, restaurant and outdoor areas were very nice.
We were only there for one night, arrived around 1:30 and planned to drive on to Orlando the next day. The weather was cold and windy on arrival day--way too cold to swim. We walked on the beach and had a great dinner at the Atlantic Ocean Grille on the Cocoa Beach Pier. The next day we had brunch at the Three Wishes Restaurant at the hotel, changed into swimsuits and packed up the car. Then we spent the afternoon on the beach before rinsing off, putting shorts on over our suits and heading to Orlando. The weather was much better--although the water was still too cold for me. My ocean-loving daughters didn't seem to mind and we had a great day.
I agree with one of the other posters that when we are used to the pristine Disney-style vacation, many other places seem dirty and tacky. This was really proven to me with this trip where we were offsite at WDW. Our hotel in Kissimmee was beautiful and very clean, but we were offended by the cheap souvenir stands and such. We really have been spoiled by Disney!!
Thanks for all the great suggestions. I am taking notes for our next trip!
Sher