From my experience growing up, this is the best spot to watch the launches for free:
http://www.titusville.com/Page.asp?NavID=211
(Rotary Riverfront Park 4141 S Washington Avenue (US1), Titusville)
Get there early in the morning (or as early as it will open if it's a morning launch) to grab one of the parking spots in front of the water (use the south parking lot with the pier, as the north one has an obstructed view). This site is fairly unique because it seems like you have lower vegitation on the other side of the river to look through from this angle, giving you a superior view to most other free locations.
Here's a photo I took from this park of the last launch:
Alternatively, you can park at Paul's Smoke House restraunt for a fee ($10 roughly). The catch is they don't start letting people in till a few hours before launch. By that time all the good parking spots are taken and some have resorted to waiting in line at Paul's just to get in. There is usually sitting room available right up to launch though, so I would have it in mind as a backup plan - the trick is to park at the mall across the street on US1 and walk it. For the best view where you're not looking over a stranger's shoulder, grab a spot early and hope they don't scrub. You should plan to be here for at least a few days (long weekend perhaps?) to increase your odds of seeing it launch.