What about firing the rocket from Jules Verne's space gun[0]?
Now, I don't mean an actual gun what with the high g-forces and so, but only some machinery that gives the rocket high initial speed. Maybe a super sonic evacuated tube maglev that ends with a ramp?
Put it on Mt. Everest for less air resistance.
You still get a massive hit from the atmosphere when you exit the tunnel if you've built up any significant speed. Air pressure up there is still a third of air pressure at sea level.
[0] http://en.wikipedia.org/wiki/Space_gun