I agree, definitely take some time on your first trip to drive to some of the resort hotels on Disney property and check them out. Especially the Boardwalk, Animal Kingdom Lodge, the monorail resorts (Which I would take the bus to MK and then hop on the monorail to resort hop, and take the boat over to Wilderness Lodge). You won't regret renting a car. Coming and going to wherever you want, whenever you want gives you much more freedom than having to wait for a bus. Many have complained of full busses and having to wait for one with enough room on it. That wastes valuable time.
Also since this is your first trip, know that when visiting these other hotel resorts that they all have entrance gates, just tell the attendant you are going to do some shopping or eating at a restaurant and they will let you through (except at the MK resorts where you usually need a dining reservation in order for them to let you park there so this is another reason why you should take the bus to MK first to see these particular resorts). But with as many days that your trip will be, visiting the Boardwalk and other resorts will definitely be something you will want to do and renting a car is definitely the best way to see them.