Others have mentioned it, but I'll plug it again. I would seriously consider Trail's End at Ft. W. It's cheaper than most WDW restaurants, the food is good and it's simple. Plus the whole atmosphere at Ft. W is unique IMHO. The WDW stables are right next door so you can visit the horses (and take a pony ride if your kid's are short enough), visit the general store and play on the playground. Ft. W is easily accessible by boat from WL, MK and CR.
If you are looking for Italian (you mentioned Tony's), consider Trattoria al Forno on the Boardwalk or go to Via Napoli in EP where you can keep costs down by sharing a pizza, a salad, etc. Spice Road Table is also excellent. Really good, huge steak (portions here are gigantic). For a family of four, you could split two apps and two entrees and have more than enough food.