I know you are against it now, but I really recommend renting a car. For several days worth of renting, it would be more than the $175 price you are being quoted, but possibly not much more, plus you get to keep it longer and you can decide exactly where you want to go, rather than possibly some area you don't want to be dropped off at. If you can find a one-day rental, it would probably be quite a bit less. And you can pick up/drop off on WDW property at the Car Care Center or at the Dolphin Resort.
If you want a nice stretch of beach in Cocoa Beach that's not too crowded (also fewer restaurants, etc.), go south of 528, 520 and even Minutemen Causeway, and park at one of the beach front metered parking areas on 1st through 5th or so Streets South (numbered streets go west to east, generally ending at the beach). You'll pass all the touristy stuff (Ron Jon, the high rise hotels, etc.) and go by a "Welcome to Cocoa Beach" sign before you get to this point. Very quiet there and the beach is quite wide. We prefer the 4th Street S. lot. Remember, there's not much there in terms of services, stores, etc. here so bring what you need with you if going here.
As for driving in busy areas, getting to Cocoa Beach from Orlando, even WDW area, could hardly be easier. Just get on the B-Line (528) headed east. You may need to get on I-4 (headed east) a few minutes to get to it, but it's really not bad. 528 tends to be a very quiet road, though it is a toll road. When you get to Cape Canaveral, turn right when you come to A1A (the beach road), and Cocoa Beach is just down the road.
Budget about 80-90 minutes each way.
HTH.
