I know what you're talking about. I still have a pair of the old Bata Bikers with holes worn through them. Too bad such shoes have gone out of fashion.

I did a search at Nashbar and found one shoe that might meet your qualifications if you wear size 39 (and marked down to $9.99).
http://www.nashbar.com/profile.cfm?c...%20BMX%20Shoes

I vaguely recall someone on this board recommending a shoe a few months back. Perhaps a thread search will turn something up.

Maybe there's a way to take a sneaker and put something stiff inside under the insole?

Good luck in your search.