On Davis Island, as another poster says, there are no chain restaurants, just independent owner-operated restaurants, most with sidewalk cafes, and all located on the Island's 'restaurant row' which is along East Davis Boulevard. Among the many places available, the '220 East' steak house offers almost all it's dinners at under $25.00 a plate, and most of those are under $20.00. -- However, any wine or cocktails are extra, and as I don't drink I cannot comment on the cost of such beverages, but I can attest to the great food. They have an enormous wine selection, for a place this size, and my friends who do imbibe tell me that the wines are excellent. They have a bar, as well, and serve cocktails at the bar, or at your table.
Also on the Island is Estela's, a Mexican eatery, with a separate dining room in their bar, as well as a great sidewalk dining. Most meals come in at between $10.00 to $20,00, and the portions are ample enough to require a doggie bag for take-home, which you will want to do because the food is good enough to leave none behind. The owner is actually from Central America, and her take on Mexican fare is slightly different, and always for the better.
Also on the Island, and also with meals under $25.00 and sidewalk dining, are Rick's Italian Cafe, as well as Tate's (also Italian, with something of a 'beer-by-the-pitcher' atmosphere).
The Plum Tree (Oriental) restaurant is mostly take-out, but they do have some inside tables, and a few on the sidewalk, as well. Their food is quite good, and always economical. Unlike the other venues, the Plum Tree does not offer any alcoholic beverages.
There are many other places here. A trip to the Island is worth it for the wide range of ethnic restaurants, and the casual atmosphere.