Burgers: Balls Hamburgers (Snyder Plaza -- north of SMU, and another at the corner of Midway and Northwest Highway)
Home Style: Celebration (on Lovers Lane between Lemmon and Inwood -- small place and gets crowded, but worth 30-45 minute wait)
Steaks: I think Bob's Steak and Chop House is generally considered the best steak place, but Del Friscos runs a close second. Bobs is on Lemmon, and Dels is in North Dallas -- check the phone book.
Mexican: I have it on good authority that one of the best authentic Mexican places in Dallas is at the corner of Inwood and Forrest in North Dallas (northeast corner). I don't know the name, and I haven't been there. If a little less authentic will do, you can't go wrong with Mias on Lemmon and Rafas on Lovers Lane. I don't drink, so I can't tell you who has the best margaritas, but I don't think you will have a problem at either of these two places.
Barbeque: Peggy Sue's on University in Snyder Plaza. Ate lunch there today. Pretty small, but should be ok on weekends. For Ribs, I would venture north to Lewisville near Vista Ridge Mall for Tony Romas. Red, Hot and Blue serves Memphis style BBQ, but I can't think of where a Dallas location is. Look it up in the phone book.
Italian: Spagetti Warehouse in the West End. Enough said.
Pizza: Well, some people like Campisis -- 2 locations, 1 on Mockingbird, and 1 on or near the corner of Lovers and Inwood. It is flat crust, oval shaped style pizza with plenty of toppings. I can deal with it, but it's not my favorite. Nothing deep dish comes to mind.
That's about all I can recommend. Other Dallas area folks I'm sure will chime in, but I can vouch for all of these places unless otherwise mentioned.