The onsite -- at Morningstar not the Cove - restaurants are Havana Blue - and Coco Joes - you will need to venture out for any variety - best to have a rental car - you can take the ferry shuttle to town in the daytime.
Pueblo Supermarket - Gourmet Gallery are both close by by car in Havensite for food - Costuless and Plaza xtra are a bit farther away - 10-15 min ride and worth the ride if you are buying more than snacks and occasional drinks.
Kmart is close as well and has some food and drink departments that are good prices for what is there.

Ditto exit zero's post - Frenchman's Cove villa's have full kitchen's, so cooking your own meals is an option. Check out Cuzzin's Restaurant on Back St. They have great Caribbean food, reasonably priced and good service. It can be difficult to find parking downtown, so do not park illegally, the police do ticket violators.

We have been to St. Thomas 3 times, and tomorrow we fly there for our 4th trip in 5 years!!! You will absolutely love it.....that being said, here are my words of advice

1. You MUST have a rental car to truly enjoy the Island
2. There is a place called Price Smart near the Tu Tu shopping plaza - best place to buy your food/booze - there is also a grocery store in Red Hook called Cost U Less that has great deli meats and even prepared meals.....There is a KMart in the Tu Tu Shopping plaza that also has great prices on alcohol and even has food....
3. Places to eat - there are some great restaurants in Frenchtown - most notably Bella Blu (that is our favorite). Fat Turtle is a great place to eat - very casual - down in Yacht Haven......Duffy's Love Shack and Mim's Bistro - to name a few.....

Cruise Ships are in town Mon, Tue and Wed so I would recommend staying away from downtown on these days unless you don't mind sitting in traffic and dealing with lots of crowds....

4. Take the tram up to Paradise Point - it's cheap - and catch a sunset from the restaurant at the top - beautiful 360 degree views of the VI

5. Megan's Bay is a must see - gorgeous beach, very calm water - a bit of a ride from where you are staying but worth it

Enjoy and have a blast!!!! It is a wonderful place to vacation - if you can't relax and have fun in St. Thomas, you can't have fun any where....

Costu Less is not in Red Hook but very close by Price Smart has much the same selection and prices, and does not require a membership fee - I believe the deli and meat counter in Red Hook you are referring to is Marina Market.
The cruise ship schedule is not M-Tu-Wed but varies by week and season and is published ahead of time and weekly.
Frenchtown has great restaurants!
If you have a rental car you can easily drive up to Paradise Point - the tramway is not cheap even with local ID.
Magens Bay is absolutely beautiful .

thanks for correcting me Exit! It's been 2 yrs since I've been on the island - but I'll be there in the morning for a week so my memory will get refreshed

Exit Zero - Is the road up to Paradise Point just beyond Al Cohens? Is it marked? How is the parking up there?

Yes - alongside the N. edge of the Al Cohens parking lot. Plenty of parking.

You will love the Cove....the beach isn't the greatest at the Cove but you can take the Marriott shuttle over to the Morning Star Beach, it is a pretty beach. Check with the consierge (spelling?) at the desk, the last time we went up the tram, we got a good discount by showing our Marriott room keycard. Not sure if they still do that.. Magen's Bay is one of my favorite beaches, Sapphire beach is also very nice. As far as restaurants go, Oceana is very good, Banana Tree is good also. Not sure when you're going, this may be a little late in coming, if so, sorry!