I would also go with Rancho if that's what your family really likes. However, if you're looking for something new I would go with either the Plaza Inn or the French Market (for CS) or Cafe Orleans or Carnation Cafe (for TS).
Plaza Inn has amazing fried chicken. The pot roast is also pretty good. I haven't been very impressed with their pasta dishes (bland, with mushy pasta).
French Market has a variety of good options. I like the French Dip sandwich and the French Market chicken. The beef stew has good flavor, but the portion is small and it's mostly bread bowl. Next door to the French Market is the Mint Julep Bar, which as the Mickey beignets.
Cafe Orleans, like the French Market, features a creole/New Orleans-themed menu. It recently got an overhaul, but my favorite gumbo and pomme frites are still on the menu. It also serves the beignets and is a great spot for people watching. The monte cristo is a very popular item, but I find it to be very heavy.
Carnation Cafe features American comfort foods. I like the fried pickles and the meatloaf. The portions are pretty good sized.