You can try searching for public transit apps specific to the cities you'll be visiting. Depending on where you'll be travelling, there are some nice ones that have built-in maps of the transit system, trip planning, and real-time departure estimates. For a city like San Francisco, you may need more than one to cover the various public transit providers available (BART vs MUNI, etc). Lacking a specific app, you may want to just bookmark mobile versions of the public transit provider's website.
I also like installing a maps program that can make use of offline data. On Android, there's OsmAnd. That way, even if you no longer have data service, you can use the GPS to get a sense of where you are and what's nearby.
TripIt can be nice for keeping your travel itinerary easily accessible -- but of course it's always good to have hardcopies either on your person or in your carry-on.
Good luck!