Kennedy Space Center is Disneyland for nerds. It's located near Orlando, has rides, exhibits, and isn't what you wanted anyway.
When buying tickets for a Shuttle launch the most important thing to do is to know somebody. Whether you want the big air conditioned room or the site with the big clock you need to know somebody who can set you up.
If all you want is to be nearby then Kennedy Space Center is a good place. Even then you should probably buy tickets there and come back later for the show. I bought mine over the internet and got some rather lame tickets. There's yellow, blue, green, and purple tickets. The colors get you on tour buses to show you the rest of the structures on the island. All except the blue ticket. The blue ticket gets you in and that's it. I had a blue ticket.
Shortly after writing this I intend to drive back out and see how many of those roads are publicly accessible when it's not a launch day.
The latest you want to get there is three hours before hand. They start closing the roads two hours before hand. I left my hotel about 10:00 and got parked a little after 11:00. About the time the traffic passed over highway 1 it stopped. We then crept along for another 45 minutes before getting parked.
There are museums, displays, rides, and overpriced vendors everywhere. The museums don't really cover much you won't see at the Air and Space Museum in DC or the Cosmosphere in Hutchinson, KS. But this place has several old rockets standing or lying about outside. There are capsules, modules, and gangplanks you can climb in and walk along. There's a truly awesome kiddie play area. There's a shuttle replica you can walk through and see what they look like inside. There's a large building with a launch simulator ride. I'd suggest doing all this when it's not a launch day. Yes, KSC is open every day but Christmas but on launch days there's lines.
The main show floor has a big, but not really all that big, TV and bleachers you can sit on. You can sit out in the Florida sun and bake for several hours while you protect your spot and watch NASA TV. And when the Shuttle finally launches behind those flag poles off to the left there's a big honking tree in the way.
I picked a different spot. I found a place on the good side of the trees AND in the shade. And I only had to sit there for 3 hours protecting it. Because once people realized I had a good spot everyone else wanted in, too. It was along the sidewalk that runs along their pond. In the pond are several large turtles, softshelled tortoises mostly, and a couple of alligators. But as launch time approached the railing along the pond filled up and I had to join them or lose my view.
You can't see the launch site from KSC. But if you pick a good spot you can see the trees that the Shuttle will launch behind. Then you see a column of smoke with a bit of flame at the top. A good eye can make out the rocket boosters. Kind of anti-climactic. It's really much better on the NASA site or via YouTube.
After the launch I hit one last museum that talks about the nature preserve on the island. Everybody was leaving, traffic would be awful, why not find something better to do? When I finally got back to my car I sat and read for more than an hour before heading out. I waited until the main driveway was clear. But it wasn't long before I hit the car blockage again. I missed the turnoff but didn't really care. That was until 15 minutes and a mile later with 8 more miles to go before the main highway. I turned around to the road I really wanted. I got several miles before that jammed up too. But I only had two miles of jam to sit through.
Anyway, I was there, but I don't feel like I was there. Probably the best thing to do is rent a boat and get as close to shore as you can. You'll get a better view.