(from a fellow Houstonian...)

I know you said you didn't want a resort but I'd still suggest you take a look at Secret Harbour. We stayed their a couple of times when our kids were younger and it was great. The beach is right outside your door (if you have a beachfront condo) with great snorkeling right off the beach.

It is also just around the corner from Red Hook which makes it easy to take a ferry over to St. John.