Something like Mapfactor Navigator should punch your ticket. Free (downloadable) Open Maps, it can use your GPS and develop a trace of where you go. If your tablet battery will last two hours, you can ride for two hours and record it all.

There are downsides, of course:
- Navigation is pretty lousy with the free maps. You'll need to punch in your own locations, and develop your own routes, if you need help actually navigating!
- Most tablets aren't good for a day-long ride. They're built to read a half hour a day, or something lame like that.
- Displaying your track may be an issue.

I understand the constrained budget, but if you can spring for a hundred bucks or so, you can get a "real" GPS from fleabay or craigslist that fixes all or most of these problems.