I have the inexpensive pay version of osmand (it's osmand+). A one-time fee (maybe $6?) to download any number of state or region maps. And I purchased the countour and elevation overlay (maybe $2?) The free version has a limit of 10 state downloads.
If I'm doing driving directions, I normally use google maps if I have a data connection. They have updated traffic and better routing calculations. But osmand is fast to load and uses the previously downloaded map files.
If your phone has a separate data card, configure Osmand to store it's maps there. If you have a lot of states, it adds up to quite a bit of storage. I have 2.5 GB with maybe 10 states loaded.
Here's an example of
osmand screen shots, Mount Mitchell, near Asheville NC:
EDIT--July 2017: There are a lot of improvements in the display. I like it. For instance, making it easier to create a bicycle route to a destination address or by picking a point on the screen. There's a lot of features, so some practice with the menu options before traveling would be a good idea.
zooming in. The elevations are in meters, not feet. It shows different types of roads in different colors, and bike trails show in dark blue.
Note the map scale at the bottom right corner, menu button at bottom left. "12 of 20" gps satellites in view, gpx recording of my movements is 'off', 522 feet is my current location's elevation.
EDIT 2 -- Feb 2018: I checked these screen shots with the newer osmand version. The restroom icons don't show up until it's zoomed way in, otherwise, it looks quite similar. The icon to switch map views between driving, bicycle, and walking shows different map views, with more trails showing on the walk view.
Contour lines every 10 meters (33 feet). The setup lets you decide what zoom level starts showing contours.
Now, the bicycle and walking views show contours at a larger zoom than the driving map shows.
Zoomed way in, with a location marker that can be named and saved. More details appear as you zoom in--the museum building and bathrooms symbol, for instance.
