I've now done all the Menu items as follows:
Quit : finishes the game
Music On/Off : tweaks the music flag, though no music is currently implemented
Inventory: enters the Inventory scene (which cannot be saved)
User Save/Restore : uses 4 possible local files to save/restore any position
Android Save/Restore : to deal with situations where Android OS does something outside the game's control - e.g. Change orientation; Pull a different Activity into foreground; Destroy game for lack of resources.
In this case, the game saves its current position with the Android's own memory of the game, and restores it when the game is restarted.
All tested on both the PC-based emulator and on a Xoom device.