As for something you can easily get your hands on, micrometers are incredible. A simple screw and graduated markings on the shaft and nut give you incredibly precise measurements. You can also find mechanical calculators (adding machines) on eBay. But those really aren't very sexy examples of the concepts.

Analog computers aren't very common anymore. Your best bet is visiting one of the computer museums that house antique machines. Or watching YouTube videos of people showing them off. There's plenty of mechanical flight computers in particular on YouTube.

If you have access to a 3D printer, there's plenty of mechanisms one can print. The antikythera mechanism is a very interesting celestial computer from ancient times, and 3D models exist online.