Pushcart (which is the restaurant where Pirates Cave used to be) does not open until 3pm.....but it is definitely worth checking out, really good food and drinks, and killer view!
The pepper shrimp and jerk sausage are delicious and they have probably my favorite rice and peas out of everyone!

Oh, unless you are talking about Xtabi and then yes, they are open all day.....try the conch burger for lunch!!! Delicious!