About a 10 minute walk down the hill.
We have had good luck at the Westin, which is within walking distance if you don't mind the climb back up the hill. Big Fish (as has been recommended above) is also one of our favorites. There is a really good pizza place just on the French side (Princess Heights is very close to the border, but on the Dutch side). As mentioned above, you really do need a car if you are staying at the hotel.
Big Fish which is a nice play is right down the road, and there's another less expensive resturant right on the beach (little less expensive). The only issue is the roads are very mountainess. I'd say 5 blocks or so. I would definately recommend a car rental.
There are several close by but none are in walking distance. A car is a must!
There are some terrific restaurants nearby less than .25 miles away. And overall St Maarten is the culinary capital of the Carribbean so get out and experience those nearby as well as Grand Case.
You have to walk a good ten minutes down a steep hill and the path isn't great (plus you have to walk uphill later on the way back). There are a couple of places to eat, okay places at that.
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