From section 4 sub-section a,
You must give any other recipients of the Work or Derivative Works a copy of this License
There's no requirement of where it should be.
Google's Play Music uses some Apache 2.0 licenses. They display them in Settings > Open source licenses.
I've seen some apps have put a link called Legal Information on the about dialog which goes to another screen that has TOS stuff and links to all the third party (Apache 2.0) libraries that they use with copyright notices next to them (Ex. Apache Commons Lang © 2001-2011 The Apache Software Foundation).
For the NOTICE, section 4 sub-section d gives some clues.
If the Work includes a "NOTICE" text file as part of its distribution, then any Derivative Works that You distribute must include a readable copy of the attribution notices contained within such NOTICE file... within a NOTICE text file distributed as part of the Derivative Works;  within the Source form or documentation, if provided along with the Derivative Works; or,  within a display generated by the Derivative Works, if and wherever such third-party notices normally appear.
So if the library has a NOTICE you need to include it in one of those three places.