Savvy:
We have stayed on different parts of the island - by design. And we have found that each part has its own unique character. Literally, it is like several islands in one. Andynap has stayed beachfront on Flamands, as have we (Isle de France). That is a unique experience - you feel as though you are a million miles from nowhere in a cute little seaside village. On the other hand, St Jean has all kinds of things going on. Columbier is high in the hills, quiet, breezy and with views. Pointe Milou and Mont Jean are out over the ocean, waiting for the next tradewind to bring Columbus passing by again. Cul de Sac is actually quite pretty with the twinkling lights at night. Toiny and Grand Fond have that Away From The World feel with Grand Fond particularly being a throwback to the Chickens, Goats And Fish days of St Barts when subsistence farming and fishing were the only industries. Gouverneur and Luren are quiet and a stone's throw from town or beach. And Vitet and Lorient cap the whole scene off with great views and serenity.
You have to drive the island to get a feel and for the first several trips, Kevin's view of Accomodation Promiscuity has much merit - stay different places for your first several trips and get to know different parts of the island.
I am now at a point that if I know where a villa is, I pretty much know a lot of what to expect. The only question I need answered now is the all-important How Private Is The Pool Deck? After that, much of the rest is details.
I am sure there are some dogs when it comes to villas on St Barts. But most of the places that get a lot of airplay in this site are tried and true and have their fans based on the experiences of experienced visitors. In many cases, we are down to quibbling about subtle points such as "In the winter, there is no sun on the pool after 3PM" or "I thought there could have been a better food processor in the kitchen". Such is the level of comfort that we come to expect that even these details are noticed.
A good driveby can give you a feel for the environment, the accessibility, what is around, etc. Occasionally, you can even contact the owner of a villa and if they live on island, they will show it to you if it is empty. That is always a great thing to do when you can - a walk through. We did that with Rosita and booked La Baleine on the spot!
As to which part of the island is my favorite, I dont think I can answer that because I have loved everywhere that I have stayed. Each place has been magic in its own way. So drive by places. Indeed, tour as much of the island as you can. And go ahead and contact some of the owners who rent their villas directly (through the villa by owner link on the front page). If there is a time that their villa is open and they can meet you there, I imagine that many/most of them would be happy to show you around.
Bon chance.