I live just down the street when I am in town.
A few faves-
Jauja, the best ice cream in the world- Cervino 3901 https://www.facebook.com/pages/Jauja/102937963127558
Las Pizarras- crazy good restaurant, probably not with the kids, though- the owner is kinda uppity- but the food is world class- Thames y Charcas
http://www.tripadvisor.com/Restaurant_Review-g312741-d1751880-Reviews-Las_Pizarras_Bistro-Buenos_Aires_Capital_Federal_District.html
Punto y Banca- good Argentine Pizza (no pizza wars, please) including great fuggazetta, down on Honduras and Madrano
http://www.guiaoleo.com.ar/restaurantes/Punto-y-Banca-920
I really like Oreja Negra, a mellow nightclub with tables, light snacks, cheap drinks, and great bands- its a 15 minute walk or so, on Uriarte right by Cordoba
http://laorejanegra.weebly.com/
but that would definitely require a baby sitter.
The Sivori Museum, on the other side of the Gardens, is a really great little museum in the park, and around the corner from the museum, on Dorrego, are a couple of outdoor stands that make killer choripan (sausage sandwiches) and bondiola (barbecued pork sandwiches) eat outside on a picnic table, cheap and good.
http://pickupthefork.com/2011/01/09/parrilla-for-breakfast-the-only-ba-street-food/
http://www.museosivori.org.ar/
lots of other great museums very close- I always go to Malba, the Museum of Decorative Arts, the car museum in the Auto Club building, the Evita Museum (great restaurant there, too) and the ZOO! I love the Zoo- real carpinchos, the largest rodent in the world, swimming and climbing trees.
Plus, you should check out what is at La Rural- sometimes its an art fair, or food, or fashion- but often very fun, with samples and events.
http://www.larural.com.ar/
lots of good shopping nearby too.