You can download a free set of contour maps from a walking site. Unfortunately I have lost the URL as I now have TOPO but I am sure with a little bit of googling you should be able to find it
I have not found good trail maps, however I do a lot of geocaching with the nuvi 350 with just the city navigator map. There is a GSAK macro by pilotsnipes and another by jjred which process the pocket query and uses the POI Loader to place cache descriptions, hints, alerts, logs onto the Nuvi.
Shonkymaps provides a basemap and transparent map while Contour Australia is a transparent map. Contour Australia should work well on your Nuvi with City Navigator.
GSAK is good to have as suggested by a previous poster.
If you are really keen, I would suggest getting a Garmin Oregon or Dakota using the topo maps mentioned above with Open Street Maps free maps: