Garmin eTrex series runs on AA batteries... but not sure if you can run the typical street style navigation on them.
It looks like the Montana series and maybe the Oregon series will do that - either on an Lithium or AAs.
https://buy.garmin.com/en-US/US/cata...Product=518046
I use the eTrex20... but I do alot of offroad in addition to onroad, so I'm building routes at home, and loading extra tracks / options for use on the go.
I have no idea how well the Oregon or Montana series work in the rain (touchscreen)...