There are certainly shops and restaurants within walking distance, but you will need a car on St. Maarten. None of the best beaches are nearby, and most of the best places to eat are fairly far away. This isn't the kind of island where you can just stay on resort grounds and really enjoy yourself (at least in my opinion).

I don't drive and travel alone. I've been to SXM many times without any problems getting around without a car (including a stay at Simpson Bay Resort as well). I just keep a certain amount of cash for the week for cabs and plan my activities carefully ie, I wouldn't take a cab to Mullet Beach then one over to Grand Case in the same day kinda thing.

You can take the buses as well, super cheap. Cab fares do go up in the evenings though (at lease they used to). Though if I had the choice of renting a car I would certainly do it, at least for a few days anyway.