Dallas isn't that big. The DFW metroplex is huge, and the satellite cities (including Fort Worth) may have their own zoos, museums, etc; many people think the FW zoo is better than the Dallas zoo. That said, I live in downtown Dallas, and most of my advice will be focused on what I know.
Hit up Revolver Taco Lounge in Deep Ellum. If you like cocktails, go to Black Swan Saloon before/after. Lots of live music in that area, too, as well as some local breweries (Braindead Brewing and Deep Ellum Brewing Co, to name a couple). There's also a very good BBQ place there called Pecan Lodge, you should definitely try to hit up some real Texas brisket.
I think Uptown is kind of shitty but there are a couple of good bars. Parliament or The Tipsy Alchemist for cocktails. Manny's Tex Mex is pretty solid, but if you can find a hole in the wall joint outside of the urban core, you can find better. Mercat Bistro is a little pricey but they have some damn good casual French food. Malai Kitchen is great "Asian food for white people".
A couple good bars downtown, Midnight Rambler and The Mitchell for cocktails, The Crafty Irishman for beer and Irish pub food. Some restaurants to check out, Spice in the City (Indian fusion), Ascension Coffee (coffee+cafe), and Weekend Coffee (my favorite coffee shop in Dallas). Salsa Limon is pretty good Mexican tacos and street food, probably the best around Downtown aside from Revolver. Meso Maya is a nice sit-down authentic Mexican restaurant, with an El Fenix branch right next to it serving staple Tex-Mex. Arts district and a small but nice park (Klyde Warren Park) too.
There's some great international food in Dallas, too. Old K-town has some damn good restaurants, like "No 1 PlusChicken," a Korean fried chicken joint. New K-town, the heavily Chinese areas, most of the Japanese restaurants, etc, can be found in Carrollton, Richardson, and Plano. Mr Max in Irving is probably the most authentic Japanese izakaya I've found in the US.