Nothing great. Blackbeard's Ale is ok but I believe others mentioned here that is it brewed in Minnesota.
I drink Sierra Nevada Pale Ale on St. John. That's about the best for me. Sometimes you can find Dragon Stout too.

Best price on STJ is either Woody's happy hour from 3-6pm with $1 beers and wells. Also Cap's Place right off the ferry dock in Cruz Bay you can get $1 Miller Lite bottles all day long. Not sure about STT, but you can always buy a liter of rum for $4 and keep it in your hotel room and make drinks whenever you want.

Try a Carib.

Caribbean beers that you will find include: Presidente, Carib and Red Stripe. You have to have lots of water to brew beer, so not many around this dry neck of the woods.

Carib and Blackbeards Ale are the only 2 "local" beers I can think of. Most places will have some or all of the following (I'm going from memory here..... from November.....so please help me out if I forgot any)

Domestics:

Coors Light
Miller Light
Budweiser
Sam Adams
Sierra Neveda

Imports:

Bass Ale
Newcastle Brown Ale
Amstel Light
Heineken
Red Stripe
El Presidente (Dominican Rep.)

Local:

Carib
Blackbeards Ale

I never met a beer I didn't like - tmax

I believe FoxyS ale is also a local ale, from the same place Blackbeards comes from. I enjoyed both last time we were on the Island.

I would second the Carib nomination - better than Red Stripe.

The Blackbeards & Foxy's in bottles in contracted brewed in the states. You can get Foxy's on JVD or Blackbeards on St Croix on tap.

I'll throw a third in for Carib. Nice lager, although I saw lots of folks with Red Stripe's in their hands.

Of course if you get hooked on Cruzan rum like I did you might not drink too much beer. 😉

Love red stripe. Good call on the rum, think I will give it a go.
Thanks for all the good suggestions.