Love Shack has really good burgers (my preference is the one in the Stockyards, though the So7 location off West 7th has indoor seating in the event of rain). The Stockyards is a nice area to spend an afternoon if you have any interest in western history - as a tourist area, it also some neat little shops, including some quite expensive western wear ones. http://www.fortworthstockyards.org/
Off West 7th is Fred Texas Cafe (burgers). A little further west on West 7th (Crockett St) are a number of newer restaurants. If you happen to be driving around, a few of them may offer patio dining, but I don't remember.
Terra Mediterranean Grill
Then, there's the Food Truck Park - http://fwfoodpark.com/ I don't think all are there are Saturdays, but maybe that's changed with spring here.