These are from my own personal experience, which only encompasses launches from the east coast of Florida. Other US launch sites include Vandenberg AFB in California, which does have some decent viewing sites (though I do not know details), and Wallops Island, Virginia (about which I know next to nothing). I also have no real knowledge regarding non-US launch sites, other than general location (Kwajalein, Centre spatial guyanais, Baikonur).
Depending on the launch details, Cape Canaveral Air Force Station offers several good viewing locations for a launch.
The Kennedy Space Center Visitors Center offers tickets to various launches, which will typically let you watch from the closest point NASA and the Air Force are comfortable allowing the public. This is typically either the KSC press site or the East NASA Causeway, which is about 7 miles from LC-39A (Shuttle), 5 miles from SLC-41 (Atlas), and about 4 miles from SLC-40 (SpaceX). The farthest point on the causeway is only about 3.5 miles from SLC-37 (Delta), which is probably quite a bit closer than you would be allowed.
If you want to watch for free, your best bet would be either Space View Park in Titusville (13-15 miles from the active launch complexes) for high-azimuth launches, like SpaceX resupply missions to the ISS, or Jetty Park in Cape Canaveral for due-east launches (9-12 miles).
If you've never seen a launch in person before, don't focus too hard on getting good pictures. You want to watch the launch with your eyes, not with the screen on your camera. I was able to get decent video by zooming out and holding the camera at my chest -- pointing it in the general direction of the vehicle.
Launch schedules only move in one direction. Plan to be there for at least two or three days after the planned launch date, plan to be there at least a couple hours after launch time, and be aware that the launch may not happen after all.
CCAFS and KSC are basically in a giant swamp. Bring sunscreen (lots -- unless it's a night launch), plenty of water, and mosquito repellant (always!). Also keep an eye out for alligators -- expect to find one in pretty much every ditch and puddle around you.
Keeping tabs on the launch
If you have a digital trunking scanner, program in the CCAFS/KSC radio frequencies. You won't necessarily get the launch control loop, especially with military or proprietary launches, but you should get enough chatter to give you an idea of how long until liftoff.
If you have 4G service, you might try following streaming video of the launch (varies, depending on launch provider). Keep in mind the stream will about 30 seconds behind real time.