July 14, 2015 11:49:57 UTC (07:49:57 EDT) is the official closest approach time, when the spacecraft will pass 12,500 km (7,800 mi) from Pluto. This is a little more than 9 hours. As always, Wikipedia has a gallery of the various photos taken by NH.
Remember that because of the low connection speed (a few kb/s) and large time delay, images won't be sent immediately on close approach, and many high-resolution images will be sent several months later until the other, more important data, gets sent first.
NASA's official page has a countdown and other images and information. Here's Pluto and Charon:
Fun fact: The New Horizons probe escaped Earth with the highest velocity out of all the things we have launched.