Mitaka has a JR station (JR Mitaka) that can be accessed via the Chuo and Chuo-Sobu Line..
The Ghibli Museum is a very large multistorey building constructed with a different theme on every level along with exhibits and games. On top of the roof is a 1:1 scale model of the robot from Laputa, and there is a mini-theatre inside which shows a short animation from Ghibli Studios. There is a cafe and souvenir shop located towards the right side of the building.
You must book tickets using JTB, it is very popular so you must book at least a month in advance.
There is a large park nearby here (Inokashirakoen) which you can take a stroll through on your way back.