Some additional budget friendly dining options around Rodney Bay since Cruzer asked

Marina:
Bread Basket Restaurant – Good reasonable local food

Outside the marina:
For snacks at night, turn left leaving the marina a short walk up and you’ll see Joycee’s across the street, red food truck. Great for fried fish and chicken with or without fries.
Turn right leaving the marina and across from the new hotel you’ll see the food truck lot, good selection of options here.

Gros Islet:
Golden Apple Bar – Lunch for 10 -20 EC
Flavors of the Grill – Good following on TA
Golden Taste – Geared more towards tourists, but locally priced
Additional options:
On the main road in the morning is a guy with a display case on the sidewalk, best chicken sandwich in town.
Weekends along the waterfront is another place that grills (a lot) of fish outside, locals line up for it.

Rodney Bay:
Upstairs at the old mall is a food court; very local, cheap, plentiful, and good.
Razzmataz (Indian Restaurant) has takeout lunch specials, been in business many years.
For more upscale try Buzz, great food and service.

Pigeon Point:
Two local restaurants outside the entrance to the park, I don't have a preference but choose by what's on offer that day. You can often get 2 Chairmens drink for 8 EC and 3 Pitons for 12 EC.

Castries:
The food stands at the farmers market are great for a local lunch, my favorite is cow heel soup, but it sells out early.

And of course if you'd like to arrange a beach BBQ, you can always find Trendy at either the Boardwalk Bar or Bosuns in the marina