Joined: Jan 2009
Posts: 44,182
Likes: 6,420
From: New York, NY, and High Falls, NY, USA
Bikes: 1962 Rudge Sports, 1971 Raleigh Super Course, 1971 Raleigh Pro Track, 1974 Raleigh International, 1975 Viscount Fixie, 1982 McLean, 1996 Lemond (Ti), 2002 Burley Zydeco tandem
There are wireless bike computers, but moving it from bike to bike takes a little bit of time.
There are GPS units that do this. I have a Garmin Edge 200, but it's way above your budget.
If you already have a smart phone, there are very inexpensive apps that do a great job but drain the battery a lot. I've used Cyclemeter on my iPhone and liked it.