One of the owners of D&L's Texas Music Cafe on South Congress bought out the other, and it's now called "Beck's". Sunday lunch on the patio can be a lot of fun, especially if somebody as good as Red Volkaert is supplying the live music.
There's a new pizza joint just south of there called "HomeSlice". It's pretty decent NY style pizza.
And, continuing the 78704 theme, up near the corner of Academy & South Congress is Doc's Motor Works. I wasn't thrilled with my burger there, but it's a fun bar & patio for hanging out.
So is Freddy's on South 1st.
And the Paggi House has reinvented itself as a more casual bar/restaurant. Don't know if they do weekend lunches or not.
There's also Taverna at 2nd & Lavaca, and Dona Emilia's on 1st (Cesar Chavez) across from the Four Seasons.
That ought to get you started.