I would try HERE maps. It's a mapping app from Nokia and available for Android. I used it on my Samsung Galaxy S4 while offline. In order to use the app offline, you download map packs for different countries or regions to your phones hard drive or memory card.

Since I downloaded the app, I have only travelled out of the US once. On my trip to Canada, I can report that it worked pretty darn well. I downloaded the British Columbia map pack before leaving the US and was able to access the map data offline. I was able to search for restaurants and other points of interest without any issues.

It's good to note that the map data can be large. I saved the data to my memory card rather than my phones memory to save phone storage space.

I am not sure about using the app for public transport while offline. I did not attempt to use the feature, and I am not sure if the app offers it or how well it works.

There is a thread in this forum for this app: Here Maps
The app can be found of the google play store here: Google Play | HERE