Since you aren't renting a car I would suggest Aruba. The hotels, restaurants and activities are consolidated in two areas that are just a few miles apart, so travel is kept to a minimum (especially if you just stay within walking distance of your hotel's area). Marriott and Hyatt have properties on the island (I can vouch for Hyatt; I have never stayed at any of the Marriott properties there). If you are truly interested in culture, however, it probably has the least of the three islands you mentioned.

Curacao has the least developed tourist infrastructure of the three islands. I rank it second because you can also do it comfortably without a car. Most of the hotels (Renaissance, Marriott and Hilton) are in the area you want to be to enjoy shopping, dining, etc. The Marriott and Hilton have a beach but are a short car ride away from the entertainment area. The Renaissance is right in the center of things, but I don't believe it has a beach. The architecture there and the unique lifestyle give it a unique vibe/culture that you can feel when exploring.

St. Maarten ranks third based on your requirements, but if you are willing to rent a car and stay in a non-chain hotel, it would probably rank at the top simply because of the culture available on the island. Of the hotel chains you mentioned, only SPG has a property there and it is very secluded on the east side of the island. You will need a car if you choose to stay there. By renting a car you can experience both the French and Dutch sides of the islands and absorb the unique differences in culture.