Maho, Beacon Hill, Simpson Bay, Grand Case on or very near the beach, Orient, Dawn Beach. You want to be near a population center where there are resorts, and a fair amount of tourist staying in the area. This puts you in areas you can walk around even in the evening and be and feel safe with other tourist. Avoid areas that don't have resorts near by, you are a tourist and not a local, when you have been to island a few times then you can decide if you want to stay in mostly non tourist areas. Not at all saying the non tourist areas are not safe, and after you get the feel of the island you may choose to go back to one of those non touristy areas but unlikely.
If you have budget limits, speak up or pm in private to the people that you feel have given you good info.
Good luck with your choice, and I think you will find the best thing on island is the people.
Todd