Mary's Boon--right on the beach, restaurant onsite, plus Karakter next door. They have some budget rooms which are a good budget option. Pool. Great old time Caribbean feel.

Horny Toad Guesthouse--right on the beach, no restaurant, but great old time Caribbean feel.

Either one would suit your purposes wonderfully.

Or, it couldn't hurt to do a google search for Simpson Bay Resort, Flamingo, Atrium, depending on when you are going, could be a good deal.