Anuta, go to www.sbhonline.com. Here's a map of the island:

http://www.caribline.com/islands/sb/sbmap.shtml

They have a villa section there, some that can be rented directly from the owner and cut out the middle man fees. If you post what you want to spend there are regulars that will certainly help you find exactly what you want. You can also go to these websites and look around:

http://www.saintbarth.org/v/
www.wimco.com
http://www2.gobeach.com/stbarts/stbprice.htm
http://www.stbarth.com/villas.htm

You definitely want a car in St. Barts. There is so much to explore and taxis would cost a fortune. As far as being too far from the beach. Most all the beaches are within 10-15 minutes away by car and the reason most people stay in the villas is for the privacy and the views that will knock your socks off. Most of the villas have their own private pools and jacuzzi's.

If you don't get seasick the ferry is probably the cheapest way to get there. The seas from St. Martin to St. Barts can be very rough though so if you do get seasick, take the plane. To give you an idea, we are paying $188 on Winair round trip from SXM to SBH the end of April. We booked this thru US Airways. They have a partnership with Winair and were cheaper than going directly thru Winair. I don't know what the ferry costs but for us that is a thrill that we could get along without. We'd rather take a 10 min. plane ride and see the ariel views of the island anyway.

http://www.saint-barths.com/

This commuter airline might help but it has limited flights to St. Barts from SXM but if it works it's quite a bit less expensive. It does not fly to Anguilla.

http://www.stbarthcommuter.com/REGULIER_en.htm

If you look on the map, the St. Jean area is very convenient for all the things you want. So anywhere close to that area with good roads will be fine. We will be staying at the Christopher Hotel in Pointe Milou which is probaby 10-15 minutes from St. Jean Bay area. So that gives you an idea of the distance.

Now we need the Anguilla contingent to come to your rescue for that part of your trip.