As PP have said, you can go without a car as long as you are staying on Disney property and then you can use Disney transport. However, if you have a dinner ADR at a resort hotel then you will have to allow extra time if you are going to use Disney transport to get there. There are no busses, for example, that run from one resort to another. A taxi would be quicker.
Here's what allears says about that situation
If you plan to eat at many of the fine Walt Disney World resort restaurants your transportation options become more complex and definitely limiting, especially after 9pm. If leaving from your hotel, you would need to go from there to a park and then catch transportation to the hotel where the restaurant is (Unless you are staying and going to a monorail hotel). Likewise, on the return, you would need to go from the resort to an open park and back to your hotel. Once the hotel-park transportation has closed, you generally will be bused to DTD and then catch a bus (or boat) to your hotel. As you can see, this does take quite a bit of time. A final option would be to pay for a taxi back to your hotel.
Check this out-it could help you decide.
http://allears.net/pl/transp.htm
Also, if you want to see more of the "Real Florida" you'll need a car. Of course you could rent one from the CCC for a few days if you'd like. My DM insists that we don't spend everyday at Disney. We have visited, and enjoyed for the most part, the following in our trips to WDW: Anna Marie Island, Sanibel Island, Honeymoon Island, Merrit Island Refuge, Discovery Cove, Busch Gardens, Rainbow Springs, St. John River, Crystal River, Hommassa (sp?) River, St. Augustine, some other springs, visting with my DM's aunt and uncle in Orlando, etc. For us a rental is a must. Also we stop to pick up breakfast, Diet Cokes, waters, etc. on our way to POP from the airport. If you're not on
DDP having a car will give you more options for dining. For example, the McD's on property do not have the value menus most McD's do. There is one located not too far from AK that is a regular McDs.
One of these times I plan on trying the bus from POP to MK. Everyone says it's quicker. But then the way we do it works out nicely too. For example, if we are going to MK and Epcot the same day I will park at the location where we will be ending our day. Usually Epcot. So we park at Epcot, take the monorail to MK (switching at TTC) and then when we leave MK we do the reverse. Monorail to Epcot. When we leave Epcot we jump in our car and go. Pretty slick!
If you are staying at a MK resort eating at other resorts is a little easier with the monorail and boat options.
Car rental rates are up this year. We are paying $363 for a full size for 11 days. In the past I've gotten a minivan for about $250 for 10 days. Hoping rates will start to fall as my trip gets closer.
HTH.