I want to point out that the location you are referring to is a Courtyard by Marriott. This is important, as there is also a Marriott resort which is closer to the tender dock. And due to beach erosion, the Marriott Resort has a very narrow strip of beach right now. So, make sure you specify Courtyard.
While this property was still a Holiday Inn, I read about many people going there and for approx. $10 getting a chair and bottle of water. The beach immeditately south of the Courtyard is the Public beach which is no charge. There are no lounge chairs. But I believe there is a small slide/ play area for kids. And there are some picnic tables on the beach, away from the water.
There are public accesses to the beach all along Seven Mile Beach. You don't have to go to the Public Beach or to pay at the Courtyard, but you can't use the lounge chairs at another resort -- only the sand and the sea. Another poplular spot is the governor's mansion which is immendiately north of the Westin. Although it's popular, it may be less crowded than the Courtyard.
It just depends on whether you just want to enjoy some sand and to swim, in which case you can go just about anywhere. Or if you want use of lounge chairs and beach bar, etc. then your best bet may be the Courtyard (assuming they still offer this service -- maybe someone who has been there since it changed hands in January can verify this).
As for Cemetary Beach, this is a good spot if you would like to snorkel, in addition to enjoying the beach. It's just north of Seven Mile Beach. There are no facilities there but it is a good spot to be able to snorkel from the shore. Another good snorkel spot is Eden Roc which is just south of the tender dock (you can walk to it from there). It is not a beach at all -- it's rocky, but there is a dive shop from which you can rent snorkel gear and it is good snorkeling (and convenient).