Blue piano is a stones throw from there, on Harborne Road. Families welcome, Singaporean/Thai style.
The mailbox is a short taxi ride away and has a selection of restaurants, as does the cube.
For posh food Simpsons is walking distance, but for the sake of a £3 taxi, I'd get a taxi with kids. Great lunchtime mini tasting menu with wine. Families welcome.
Then there's the rest of the city centre. Avoid Hagley road and broad street for food.
Have fun.