A car would definitely help. Before you make any plans I would call the grand cypress. The web site says "Transportation is available to local establishments in the immediate area through Mears Transportation for a nominal charge, including transportation to Downtown Disney, The Crossroads and more." (Shuttles to disney, universal, and sea world are free) I would find out what that fee is, where they go, and if it is a cab or shuttle bus. If it is a cab, Mears has plenty of vans that will fit 6 people. If you are planning only 1 or 2 trips away from the hotel or the theme parks, provided it isn’t too far, the taxi trips might be cheaper. For most of the outlets and restaurants near the grand cypress you would probably pay about $10 each way. For International Drive or universal it’s probably about $30.
Two more restaurants that haven't been mentioned are the Mucky Duck and McT's. The Mucky Duck on Captiva is one of my family's favorites. It is a must eat place anytime we visit. We tend to go there for lunch, but dinner is really good. It started out as an English Pub and always has good seafood. It's right on the beach so ask for a table by the window. McT's on Periwinkle has good early bird specials of prime rib and fresh seafood.
As rudykins said, the grand cypress is kind of in the middle of no where. You will have to take a taxi if you want to go anywhere except Disney. I don't think there is any public transportation that stops at your hotel. Most of the restaurants around Disney are geared towards tourists. One place that I used to go to is Bahama Breeze. It is located on Vineland Rd near I-4 and SR535 (about a 5-10 minute taxi ride). Bahama Breeze is a chain that specializes in Caribbean style foods. You might want to check out some of the Disney hotels. They have some good restaurants that aren't going to cost you an arm and a leg. You can take a bus to any of the Disney hotels from any of the theme parks or Downtown Disney for free. At the Polynesian, check out Kona Cafe (Pan-Asian cuisine). The Boardwalk has a good brewery (I think it is called Rocky Mountain Brewery). If you would like to try African food, try Bomas at the Animal Kingdom Lodge. It has a nice buffet. There are several others I would suggest, but they are more expensive. At Downtown Disney I always suggest the Earl of Sandwich. They have a sandwich or salad to fit everyone's taste buds for about $6. Wolfgang Puck also has 2 quick service locations with tables outside. If you want unique atmosphere check out the Prime Time Cafe at Disney's Hollywood Studios. You will be thoroughly entertained while the staff will treat you like family. If you can't get in there the Sci-Fi Diner or Mama Melrose are also good. At Epcot all of the countries have sit down restaurants. Most of them are good. (I tend to stay away from Mexico and Italy because of bad service). I suggest Chef de France, Tapen Edo or Tokyo Dining in Japan, or Le Cellier in Canada if you can get in. The last two are more expensive, but worth the price (try lunch). One that most people overlook is the sit down restaurant in Morocco. It has good food and is one of the last to be fully booked.
***If you are planning on eating at any sit down Disney restaurant, especially at the theme parks, make reservations NOW. By the time you get to Disney there won't be any spots left. The 4th is one of the busiest times so reservations are going fast.***