I've worked at the Eastern Range for a few years now, and the very best location to watch a Shuttle launch is from the top of the Vertical Integration Building (mostly known by it's intials - VIB), but you need to know a NASA manager to get up there.
Second (IMO) is out on the NASA Causeway (between Kennedy Space Center and Cape Canaveral Air Force Station. The public used to be able to get there with a car pass - you needed to know someone, but they were never too difficult to get (I used to get them for visiting friends/family). Unfortunately with the current security considerations, the only way to get there now is to be escorted by a NASA or Air Force employee with a Cape Canaveral badge (and there are limitations even then).
These days I guess the public's best viewing spot is at Jetty Park.
One final thought. The very best Shuttle launch to watch (especially at the Causeway) is one just before sunrise. The Shuttle lifts off in the dark, giving that blast of light and sound (feels like giving yourself a bunch of Tarzan thumps on the chest), then moves up into the daylight. If you get the chance to witness one, you won't forget it.