Actually google maps will let you do this and would be a good choice if you are familiar with using it at home -
Make sure you are on wifi and are signed into google maps
Search for the city or general area you want to have access to offline (this space is not unlimited, but can be very large, like almost all of Manhattan)
go to the menu (top left) and go to "Offline Areas"
Then you should see "download an offline area"
Click on "Custom Area" and it should take you back to whatever you just searched for
You can zoom in/out and move the map around, the area in the square is what you're selecting, when you're satisfied with your selection, select "Download"
This is downloaded onto your phone so you need a certain amount of free space (most of Manhattan, for example, takes 225mb)
It will stay on your phone for a month and you can use it just like you normally would with google maps - search for driving/public transport/walking directions, look for businesses, check their hours etc. Just turn wifi on your phone and you can follow your blue dot along for walking directions.
Alternatively, you may not be aware but if you have Tmobile you have free international data abroad. I think Verizon will also give you the same access you have at home for $10/day.