Recently, I've found a very nice post, Using the Google Analytics API in WordPress. It's a full blown tutorial and signed by a core contributor, no less.
In this post we’ll talk about the API, authentication and firing requests to the API using the WordPress HTTP methods, about understanding and parsing the response and finally, we’ll go through some examples of how the techniques can be used to get interesting information from your Analytics account straight into your WordPress site.
The plugin GD Press Tools has internal statistics, if you want to keep everything inside your environment.
And Jetpack statistics can be queried.