I spent two weeks at the beach

[ROBINDESBOIS]

And I spent 2 weeks on the beach.
Difference?

[pjt33]

On the beach can be nautical slang for not at sea. In the sense you probably intend, there doesn't seem to be much difference; although personally I favour at, the small number of examples in BNC favour on.

[poli]

In the U.S., on the beach literally means on the sand. At the beach means staying by the seashore.

Examples: The shipwreck survivors were found stranded on the beach.

I just spent a week at the Beach. It was hot in Miami.