1. There are a bunch of old-fashioned bike computers that don't have GPS and usually don't have altimeters (but some do). Check out Cateye.
2. Lezyne makes a number of GPS-based computers that don't rely on graphical displays, so they're pretty compact. This might be overkill for your needs.
3. Sigma makes this, which uses GPS for speed/distance instead of a wheel-rotation sensor.
4. This thing from Bryton also relies on GPS for speed, but has a proper altimeter.

Using GPS instead of a rotation counter can produce spurious results when you've got a bad signal.