Check the wheels are true (with reasonably even spoke tension), the tyres are serviceable, the bottom bracket and headset have no play, the wheel bearings have no play and spin freely, the sprockets/chainwheel teeth aren't too badly worn and the gear system works cleanly and smoothly. Also look the frame and front forks over for any obvious serious rust (unlikely) and accident damage (always possible). Check the brake operation of any bike before you ride it.