Either Great Bay or Little Bay beaches are good for your purpose. Great Bay is the beach along the Philipsburg boardwalk, and Little Bay is farther down on the left if you are at Great Bay and facing the town.
Is there enough to do around there on our own? When we get off the ship, can we walk to little or Great Bay? Are there little restaurants and shopping near by to just sort of walk around the town after our beach day?
The cruise ship pier is out a bit from Philipsburg. You can walk it but it isn't a short trip. The thing to do is use the water taxi at the cruise ship facility. It is/was $5 per person for an all-day pass, although that has probably increased since they are paying more for fuel these days too. The water taxi will take you right to the Great Bay beach area, which also has a boardwalk with shops, food, bars. The main shopping street is also "right there". Beaches in St. Maarten all must allow public access for free. However, when you get to the beach people will be offering tables, chairs, umbrellas, and these are not free. Freelance servers will also work the beach and get drinks and food for you - and they work for tips. It is worth it.
At the cruise ship facility there are also a couple bars and lots of souvenir shops, as well as a large area for regular taxis, tour buses, local excursion operators, etc. It is a pretty nice facility.
Frankly, St. Maarten/Martin tours have never wowed me. Many are contrived, such as the butterfly tour. The French side of the island seems cleaner and more refined to me. Be wary of the currents at the beaches. One can easily find them self being pulled away from the beach in a hurry if you aren't careful.
For us, a stop at St. Maarten means bumming around town for a while and then sitting on the beach. But then we've been there so many times that we've pretty much done and seen it all. Speaking of seeing it all - nudity at the beaches on the French side is to be expected, with Orient Beach having a totally nude area. The Dutch side is more prim and proper.
Actually, my wife and I took a snorkeling tour during which time we stopped at Mullet Bay beach on the DUTCH SIDE. We were very surprised that there were numerous topless women there as well. It didn't bother me, but my wife was not very excited about it.