Hmmm... I'm also considering a DIY segway as an off-season project for my robotics team. We'll be paying for this ourselves (can't fundraise), so budget is a major concern. I'm still investigating/calculating, but here's my high-level analysis...
I'm thinking of using 2 CIM motors ($28 ea) and 2 AM Toughbox gearboxes ($88 ea), because they're relatively low cost, and the Toughboxes have the ability to add a second CIM motor if we decide we want more torque/speed later. Also, these were competition parts for last year's FIRST FRC competition, so I'm pretty sure I can find some used units for cheap. As an alternative, I think CIM motors with belts/pullies may be workable as a lower-cost alternative to gearboxes, plus it would be easy to add extra motors there too, if needed later.
Other major expenses will be the batteries (will most prob have to buy whatever's available) and wheels (hoping to find something useable at Harbor Freight). Metal/materials for the frameworks should be available as scrap from various places, including some I have already. Electronics/control system is the easy part for me, as I've got lots of that already, though I'm considering changing to something with an easier programming interface for the students, such as perhaps a basic-stamp or Propeller.
I've seen others do this for under $1000, but I'm hoping to come in around $600-$700. No commitments on that yet though.
Cheers,
-Neil