I concur, there are lots of free things to do at the Fair. Go to the Midway last, if at all, and then hopefully the kids will be so tired they won't care if you do only 1 ride. That's what I do and I tell them before we go that they're only getting 1 ride (I have 3 kids so 1 ride is plenty!)
I take granola bars and water that we can refill.
The Dog Show near the barn is VERY cool and free. There's usually a horse show back there too. Do all the free things in the barn area, the petting zoo, the creative arts hall, the agricultural hall (all free) and then go over to the Bird Show (free and you gotta see it!) and the Butterfly Exhibit (it does cost money but we really enjoy it).
There are a few cool things around Big Tex himself, but we spend alot of time around the barn.
We spend about $100, you can do less, but we like to eat all the weird fried stuff.
Kroger has discount tickets and Star Telegram has Press Pass member discounts, if you belong, and I'm sure there's some others I don't know about.
Check out the official site for daily info.
http://www.bigtex.com/entertainment/highlights/