You might want to build a Stirling engine – Googling will yield lots of kits for sale, as well as free plans.
Even if you don’t actually use it for anything, a nice one can be a neat desk accessory.
I’m going to make some of those flying paper lanterns (mini hot air balloons) soon.
If you buy all new parts from a local electronics supply, maybe 20 bucks. Or free if you’ve got a reasonably stocked junk box. 
Of course, if you had a reasonably stocked junk box you wouldn’t be asking so I’ll assume you’re looking to get into the hobby. This is an easy, cheap, fun, and mostly harmless project to get started with.
I say mostly harmless because soldering irons get HOT!! 
Just pay attention to the numbering of the pins on the IC if you do build it. And get a socket for the IC as well so you don’t accidentally cook it with the soldering iron.
And if you do take this up as a hobby, always remember: Heat the part, not the solder. And only heat the part enough so that solder flows onto it. Don’t cook your parts.
One of the biggest mistakes newbies make is they heat the solder and glop it onto the board. That’s an excellent way to make a cold solder joint (which is not a good thing).
You can price all the parts at Jameco (or Digi-key), but for a ballpark figure I’m thinking that it’s going to come to around $25 or $30 with shipping.
Check out http://www.dangerouslyfun.com
Lots of home made potential disasters.
I’ve been toying with the idea of making a wooden bike (including -especially - the wheels) for a while now.