As anywhere you go, be aware of your surrounding. Don't leave anything in car and lock the car.

We've being going to SXM for over 40 years. I don't carry a pocketbook, don't wear fancy jewelry, don't flaunt anything. But I do that in most places. We've stayed in Grand Case area and have walked to restaurants from the Grand Case Beach Club. The only thing we carry is a flashlight. Not that streets are dark but in some places lights are far between. Besides we use it so cars can see us.

We have driven during days & nights and it is more difficult at night. Lots of traffic at any time but especially in early evenings.

You mentioned side trip to Anguilla or St Barts. Lots of places require a minimum nights stay. One week in SXM you'll have lots to see and do.

Where you stay may be an area without sidewalks so night walking is usually discouraged.

You'll have a great time---better if you just take precautions and not worry that something might happen.