I should plug the villa we've rented both times we stayed on St. John: Andante By The Sea. I totally recommend it! A couple named Marilyn and Richard own the place, and they are fantastic hosts. They have done so much to make this place perfect for visitors, and they are always available to answer questions. Really friendly couple with a great house to share.
The villa website is http://www.andantebythesea.com/. It's hard to do justice to the place in photos, but I've made an attempt with this panorama shot (click to make it much, much bigger). The railing looks all jaggeddy because it's something like a 270-degree view merged together.
Andante has everything: amazing views, privacy, a hammock in the shade of the lower deck, a big grill on the patio, a private pool and hot tub, a sound system that lets you play music anywhere in the house or decks via your ipod, and the ability to watch the sun rise and the sun set. There's also a great breeze that keeps the place cool enough so you don't need AC. The villa sits on the side of a mountain/hill, and there's a steep trail down to the bay below (Hart Bay). Not much of a beach, but the snorkeling is rumored to be pretty good. We've only given the snorkeling there a trial run so far...maybe another year we'll really check it out.
The best thing I can say about this place is that, even with all St. John has to offer, it's sometimes a tough choice whether to go out in the jeep and explore the island or kick back at the villa all day to tan and swim.