We have taken our kids to Disney several times, and we always stay on property, and we are always tightly budgeted for the whole thing. That's actually WHY we stay on property.
When you stay on proprty, you get a Key to the World card, and that card allows you access to each and every resort in the entire "kingdom". This may not seem like a big deal, but it really is. With this access, we can stay at the value resorts and "visit" the high end resorts any time we want. Some of the fancy ones can takes hours to walk the grounds, visit the pool (Although you aren't technically supposed to swim at the other resorts' pools, the only one that actually checks your room assignment is the pool at the Beach and Yacht clubs.) They have walking access to the parks (some), and some have FANTASTIC viewing spots for the fireworks at the parks. One of our favorite things to do is pack a picnic lunch, take it over to the Animal Kingdom Lodge, walk around the safari animals, picnic out there in the shade, and then swim for the afternoon! It's wonderful! We have also stayed at the Yacht Club, and were able to take a 5 minute stroll along the Boardwalk and view Epcot's fireworks show from the bridge over the lake. It was beautiful! You can't really get on property easily if you aren't staying on property. Parking is free at all resorts and parks if you stay on property too.
There's also a little know character meet that's FREE! If you go to the Wilderness Camp grounds, and take a quick bus trip (inside the camp grounds, that's how they travel in there), and there's a free campfire singalong and movie every night and Chip and Dale come out every night and greet every guest! Its really fun and laid back, and not all that corwded. We've done this twice, and both times was easy and fun, but would have been cumbersome and such if we were off-property and trying to just get on property for that.
Trust me, its worth it.