If you live in Manhattan, KS - you live where I was born. (not that I remember too much of it - left @ 3 months!)

Looking at the cities to which Airtran flies; you might want to look at:

Sightseeing/things to do:
Boston, MA San Antonio, TX

Beach/Nice Pool:
Orlando, FLA Hilton Head, SC

A personal recommendation would be Austin TX with a stay at the Renaissance - one of our favorite hotels...but you would have to get a car. However, I was there in Feb and got one for $19 per day -

One of the difficulties you are going to have is to get a hotel with the criteria you want (airport shuttle, nice pool, beach etc) 50K points is not going to go real far. Boston is a great choice for no car, but the hotels are higher end and will use more points. Depending on when you go, the brand new Ren is running specials for $199 - hard to beat.

My only issue with DC is that it is so hot and humid in the summer - but that doesn't bother everyone.