I live in Du Pont circle and would mostly cruise the bay and short
trips up and down the coast, as well as park the Georgetown waterfront
on saturday nights.

Check how many actual miles it is from DC to the Bay. You may end up
reconsidering the idea, unless you're talking about a trailer boat. And if
you're talking trailer boat you may want to rethink the 'going to Hatteras'
idea.

I probably will waterski some, but mostly just cruise fast and
listen to music. My budget is around $15k-20k, used.

Good, fast, cheap... pick two.

One web resource to check out:

http://www.partyonthepotomac.com