If your primary goal is a kid-friendly relatively inexpensive meal, I wouldn't do the Boardwalk. We stay there all the time, but the restaurants are mostly on the upscale end. There is an ESPN Club that might be a hit if you have sports fans, and that's not too expensive, but Spoodles and the Flying Fish are definitely higher priced. There is a place called Beaches and Cream just across from the Boardwalk at the Beach Club (you could take the Boat or walk over there), and they have great hamburgers and ice cream; that's not too expensive.
You could eat elsewhere though and then wander around the Boardwalk. They do have some neat things for kids, but most of it you have to pay for....e.g., hair wraps ($1.50/inch I think); very elaborate face painting (about $8 depending on which you choose); surrey rentals (but kids have to be 60" to pedal), etc. A couple times a night they have some people who come out and do a little show for about 15 minutes which includes some juggling, magic, etc., and the kids like that. (Bonus is that it's free!) They also sometimes set-up a DJ towards one end; the night we were there a bunch of the girls were having a great time trying to hula-hoop along with the music. Finally, the Boardwalk is within walking distance of Fantasia Miniature Golf, so that would be another option.
Downtown Disney has a wider selection of restaurants (including a McDonalds), and a lot of shopping that could appeal to kids (e.g.
Disney Store,
Lego Store.)
You could also eat at one of the many resort restaurants without theme park admission. When we were there, we had a great dinner at O'Hana's at the Polynesian, and they had coconut races in the middle of dinner for the kids. The Whispering Canyon Cafe at Wilderness Lodge was also fun (stick ponys for the kids, and lots of comic relief), but the food wasn't as great there. I wouldn't classify these resort restaurants as inexpensive either though.
We did the Hoop Dee Doo Review our first night just a few weeks ago with an 8, 4, and 1 year old, and the 8 year old laughed hysterically for nearly the entire time. This is about the furthest you can get from inexpensive though (roughly $50/adult and $28/child if I remember right.) It was kind of a special night for us because Grandparents on both sides were with us, so we splurged.
Have fun whatever you decide!