Well, it depends on your schedule and your interests of course.
But, I'd start the day at Las Manitas for breakfast tacos or migas or whatever you like to eat. Then, I'd walk up Congress Ave. to Little City for a cup of coffee. After that, I would go to the Capitol and take the tour that is free provided by the guides. (I don't know if they give tours on the weekend.)
For lunch, I would go to Ben's Long Branch BBQ on E. 11th or Sam's BBQ on E 12th since they're fairly close to the Capitol.
As an alternative, I might suggest Taco Express on South Lamar or the Broken Spoke for chicken fried steak (if they're still cooking there -- I haven't been for several years).
Of course, there's always the Barton Springs pool, but it's a bit cold these days.
Then of course, there is the Oasis overlooking Lake Travis which makes for nice sunsets but they had some sort of fire or something there and I'm not sure if it has been rebuilt.
Other than that, at night, I'd go to 4th St., or maybe 6th St., and listen to music.
Other daytime activities might be the Ransom Center, the Bullock Museum, or just strolling around Town Lake and talking or jogging.
Have fun. Take them to places that you like to go to.
