Desperate in Orlando
It depends if you have a car or not. If not, you'll be pretty hard up looking for something of the non-chain variety.
If you travel North on 535 (to Dr. Phillips) and make a right on Sand Lake Road, you'll find a neighborhood area which is not replete with chains. If you like Indian, there is a great Indian Restaurant about a mile down, in the Albertson's shopping center, called the Spice Cafe. It's locally-owned and fabulous. Otherwise, just a little farther down the road is what we Orlandoans call Restaurant Row, which has a good mixture of chains and non-chains. If you go too far, you'll end up under I-4 and heading towards international drive.
Otherwise, try BlueZoo at the Swan and Dolphin. It's technically not a chain per se, but owned by Todd English's restaurant group, and is quite good. Also, though not the best, but acceptable, Bongo's at Downtown Disney is pretty good, and I enjoy the sushi at Wolfgang Puck's place.
We're FL residents, living about 1 hr. from WDW. What with visitors, we end up spending some time over there.
We've always had a good meal at Raglan Road Pub in Downtown Disney. It serves a sort of mainstream American food but with a Celtic twist. If you want to see their menu, go to: http://allearsnet.com/reviewpost/
There's usually traditional Irish music starting around 9pm & it can get a little loud at that point.
Ditto on Wolfgang's at Downtown Disney, and Raglan Road at Pleasure Island for great Irish food. Try the Heaven On Earth (it really is!) - baby back ribs in Guinness-honey sauce. It's a small portion though.
If you're willing to drive a couple of miles, take I-4 East (toward town) to Sand Lake Road, go left on Sand Lake, and that is Restaurant Row. Lots of good stuff to choose from there (try Vines or Samba Room).
THere are some options.....Dr.Phillips area has a great lebonese restaurant called Cedars, also Christinis -very high end Italian, Chathams is supposed to be fantastic but I've never been. Go to winter park area. Lots of choices of great restaurants, not chains!. If you need help on a dinner out one night, or lunch, I could help more with specifics.
The area around Disney is FULL of restaurants. First, you gotta start with Disney itself...the resorts and even parks (particularly Epcot) have some reeeally good restaurants...check out http://www.allearsnet.com/din/dining.htm for all the menus...I just ate at Jiko in the Animal Kingdom Lodge and it was great!
You're also not that far from Sand Lake, which is full of great restaurants. I love Roy's, it is a chain but I love the food and atmosphere. I've also heard a lot of things about Fishbones and Timpano's, but I was not too impressed with Timpano's and have not been to Fishbone. If you just drive down that way, you'll find tons of places. Good luck!
Thanks for your suggestions everyone!
We had a night out without the kids last night and went to Bluezoo. It was very good. We then went to Downtown Disney and had a few beers at Raglan Road. We had a nice time there.
We are definitely going to check out the Dr Phillips area. The Lebanese restaurant sounds wonderful! As does the Indian so we may hit that as well.
Again, thank you everyone for your very helpful suggestions!