Matchbox

Acadiana is very kid friendly (though it doesn't look it). The weight staff is great with kids (and they even have a kids menu).

Teaism is great - but my kid didn't really like their food until she was a bit older. And, it is very crowded and not stroller friendly.

Meatballs is good - and easy with a kid. Although, the service can be slow. It tends to get crowded depending on the time of day. Early enough...and it's very good and kid friendly.

Hill Country BBQ is really good and very easy to manage with kids. It's loud...so if your kid has meltdown, no one will notice.

Clyde's is always easy and they are used to kids running all over the place. They have a wide kids menu too.

For a stretch go to Busboys and Poets over on 5th and K - the food it a little better then Clydes. If the weather is nice you can sit outside.

District of Pi on F is also a good bet as well.

I second Austin Grill.