St Martin / St Maarten is in general quite an expensive island, there are, however, some places that do excellent cheap food.

The Lolos in Grand Case are local shacks with open grills and wooden tables and benches around them. They serve local creole food, like grilled ribs & chicken, fish or lobster with rice and peas, johnny cakes and salads. People's favorites are Talk of the Town and Sky's the limit. 

Similar to the Lolos of Grand Case  you will also find Johnny B Under the Tree in Cole Bay or Rosie's Van in front of the Marigot Stadium.

Yvettes in Quartier D'Orleans is a bit of a hidden gem, another local restaurant serving creole food and very inexpensive. Quite an experience!

Zee Best is great for inexpensive breakfast or lunch. Their pastries are excellent!