Yeah, Cocoa Beach is the closest, but what is your goal, just toes in the sand?
I tend to think that the West coast (Gulf side) of Florida has some of the best beaches. Dunedin, or St. Petersburg, has some great beaches. Yes, you have to deal with traffic getting there if you take the I4 so plan accordingly, but I enjoy that side of Florida.
You could also go to Cape Canaveral when you visit Cocoa Beach, if you're into the space stuff. Enjoy your trip!