I have a 1966 90 cc for sale right now.
eBay Motors: 1966 honda 90 ( cm90 c90m cm91 c91m trail c90 4 parts ) (item 190233060655 end time Jul-05-08 08:18:09 PDT)
check it out. It would need work, but it is probably in your budget. Starting at $10. The 90cc goes 60mph. I think the wheels are interchangable with the 70's too, but I'm not sure. If so these may have the upgraded braking system you are interested in.