For faster travel, rockets tend to be chosen. What, then, would be the point of a space elevator?
By the way, the top recorded speed of a Bugatti Veyron, the fastest production car in the world, is 253 mph - on the flat. Travelling vertically at that speed, a space elevator car (we might assume it is powered by a 1%-efficient laser-beam stationed on the ground and aimed at photovoltaic panels on the bottom of the elevator car) would take 88 hours (or 3.7 days) to get to GEO.