Noe Valley adventurous, budget-minded family
Not the most budget minded area, you are blocks away from the Mission area which you will find a better selection of restaurants that are reasonable to cheap.
The only ones I can think of in Noe Valley-
Pomelo-multiethnic menu, very good- Church/30th
Eric's Restaurant- Americanized versions of classic Hunan and Mandarin
On Church @ 27th street
Savor- American- 24th/ Sanchez
There's better food at lower prices on Mission Street between Valencia and Cortland (near 30th street). All of these are kid friendly.
Lotus Garden - Vietnamese
Pastores - Mexican
Yo's - Sushi
Inka's - Peruvian Roast Chicken
Goood Frikken Chicken - Middle Eastern Roast Chicken
Angkor Borei - Cambodian
more upscale American (and higher prices) at Blue Plate and Front Porch
My cousin and her husband take their babies to Chenery Park in nearby Glen Park.
I agree with the other poster - Noe is not exactly a food destination neighborhood. However, the Mission is - and it is an easy walk down to the Mission from Noe or you can take Muni (J train down to 18th Street and then walk down).
Places to try in the Mission based upon your criteria:
Pakwan (Pakistani): 16th b/n Valencia & Guerrero
Ti Couz (Creperie): 16th b/n Valencia & Guerrero
Taquerias throughout the Mission (I like La Taqueria on Mission & 25th or Le Cumbre - which is on Valencia I think)
Bombay Icecream - Indian ice cream joint
The outer mission is in walking distance - where most of the restaurants listed above are located. There are a couple of others to recommend:
Mi Lindo Peru - much better vs. Inka's for overall Peruvian food
El Zocolo - empanadas
Regent Thai on Church (near 30th) is very good, inexpensive and a little on the fancy side.
Mi Lindo Yucatan on 24th is my favorite Mexican food restaurant in SF. Good food, lots of it, and good prices.
Mi Lindo Peru's lunch menu is one of the best bargains in the area, IMHO. It's nearly half the price of dinner for the same plate.
Jasmine Tea House is another that has a great lunch menu - most plates are large in portions and under $5. Plus, it's a very cute place.
Lucca Ravioli is a great place to pick up Italian Deli sandwiches or Italian imports and wines for really good prices.
If you've never had papusas before, they're very filling, inexpensive, and scrumptious. There's a place on the corner of Mission and Valencia that I usually go to but the name escapes me. El Patio (across the street) also has good ones and is very comfortable and friendly, too.
Gooood Fricken Chicken is good for rotisserie chicken and middle eastern food (good hummus, falafel, etc.)
If you order the Spaghetti and meatballs at Emmy's Spaghetti shack, you'll be getting a bargain. Everything else on the menu can get pricey but the spaghetti and meatballs (one order can feed 2 adults and a child) with a big salad or side is a bargain.