Garmin Etrex 20. You can load free OpenStreetMap maps on it. It uses AA batteries, so easy to carry a few spares. Or the Garmin Dakota 10 is a similar thing, but with a touch screen.
The cheaper Etrex 10 would work for just following a route, but I think its worth having mapping to give you an idea of how the route relates to where you are.
I went through all of these options before going for the eTrex 20.
The Dakota 10 looks decent but it has a fairly small inbuilt memory and doesn’t take SD cards, which the eTrex does (as well as having a larger internal memory).
On the other side, the eTrex 10 looks OK, it just doesn’t have proper mapping, only a line to follow.
The eTrex 20 was the budget conscious option for me, without paying extra for barometric altimeters included in the eTrex 30 and Dakota 20.
They won’t have all the cycling specific functions you’ll find on the Edge units, but they have your basic trip readings (average speed, max speed, distance, elevation, etc) and they’re spot on for mapping.
Battery life on the eTrex is something like 25 hours on AAs. Think it’s a bit less on the Dakota because of the larger screen. They last me for ages, anyway.