Where is Yui stored in SAO II?
According to a Q&amp;A session1 (EX00～Face to Face～) in the third popularity contest held by Kawahara Reki, as Kunori Fumio (his webnovel penname), in 2005:

Her core program routine runs and is stored in the local memory of Kirito's NerveGear and takes up about 3TB.

1 Chinese-translated copy of the Q&amp;A session