I'll try to keep this short. I eat out too much.
On the east side: kinda tropical, de nada and Sawyer are good laid back food spots. Justines is a great French spot with a setting you can't beat. Bufalina has excellent pizza and wine... Their pasta is delicious but portions don't justify the cost. Cenote is my go to breakfast spot. If you like divey spots, the Grackle, Violet Crown and the liberty are all great. I think East Side King still has a truck at Liberty too. Grackle just got Asador tacos... That mushroom taco is absurd.
South Congress area: June's is a nice little wine bar. Joanne's and the Austin motel have good food and a fun pool.
Near the lake (not sure what to call these areas): carpenters hall has a good menu and fun pool parties. Pecan Square is a great date night/celebration spot... don't sleep on the crab salad. Fresas is casual Mexican that's elevated without ruining the simple beauty of Mexican cuisine.
I can keep going, but that's probably more than enough. Last suggestion I'll give, if you like live music if any kind, go to Sahara Lounge on a Saturday night. The house band is unbeatable.