Nassau - don't buy jewellry. Straw Market for souvenirs.
St. Thomas - more jewellry stores than you've ever seen scrunched into the smallest space you've ever seen. No tax. Higher prices than in St. Maarten. Be careful of the small, one-clerk shops. Don't buy the $150.00 "diamond" tennis bracelets. Those are industrial grade diamonds. Trust me...St. Maarten is better for jewellry prices.