Your best bet would be to contact the city marina which is just past the jettys on the port side. There are some temporary slips at the very end of the channel for loading and unloading. You may be able to dock there but otherwise you'd have to tie up at the city marina. There is a free trolley that runs once an hour but from there you can walk pretty much anywhere in town. We've had lunch at the Wharf, it was good and not too expensive. We've heard the Beach Street Station & Grill is good for lunch but have only been there for breakfast. They are closed Tues. - Thurs. Here's a link to some other restaurants in Port A.
Restaurants in Port Aransas, Texas
Let me know if you need anything else.