Hi, I would also suggest New Smyrna Beach. It is a really cool little surf village on the beach. Part of the beach allows for driving on the beach, which is nice if you have a bunch of stuff to unload, but otherwise, is something you will need to look out for if you are walking. I have seen people almost get hit many times.
The surf is hit and miss form what I have seen. I was there in April of 2012 and the surf was solid and clean. Next to the main entry point to the beach are a couple surfshops for wax, etc.
I have been skunked more times than I can count on Florida surf in general though. Perhaps, you might want to be prepared to grab a body board or even a skim board if the waves are gutless.
Also this is a fairly sharky area of the US, so be aware of the landlord in the grey suit.
P.S...the truly closest place to surf in proximity to Orlando would be Typhoon Laggon at Disney where you can surf the wavepool before or after normal operating hours...though I can't vouch for that
Andy