I assume you mean closest to get to by car, and not as the crow flies. That is the more practical question.
On the East coast, I would guess Cocoa Beach, which is very nice. On the West coast, I would say the beaches on the Clearwater/St. Pete peninsula (Clearwater Beach, Indian Rocks Beach, Madeira Beach, St. Pete's Beach).
East is closer. East and West have very different characters. I prefer the West coast. Where you would prefer depends greatly on what you are looking for. Privacy on one extreme versus well-serviced and heavily life-guarded on the other.
I'm sure people on here will give you widely different advice, but it really depends on your personal preferences.