A highly advanced city built in Hakone, designed to replace New Tokyo-2 as the new capital of Japan. This may have been just an excuse to fund its astronomical construction costs, as the city itself was actually designed as a fortress to counter the looming threat of the Angels.
Built upon a massive subterranean cavity called the Geo Front, the city has the unique ability to lower its high-rise structures underground during attacks, dubbing it the Ceiling City. Among those structures are military support facilities called Armament Buildings, which are used by the Evangelion Units during combat.
Although a number of residents do live in New Tokyo-3, the majority are somehow involved or employed by NERV. The city was apparently evacuated as soon as the Angel attacks began, and has appeared desolate in most scenes throughout the series.
As described by NERV Vice Commander Kouzou Fuyutsuki, the majority of the city's functions are automated. Everything from traffic lights to city politics are controlled by the MAGI Super-Computer System located at NERV Headquarters. The city itself was modeled after the human brain, and key facilities such as hospitals are named after various regions of the brain.
Based on Neon Genesis Evangelion Platinum: 05 DVD Booklet
New Tokyo-3 has seen significant enhancements in the 2008 feature film Evangelion: 1.0 You Are (Not) Alone. Among them are several new scenes that show in detail the mechanics which allow its buildings to be retracted.
More importantly, in the film New Tokyo-3 is much more populated, and many scenes which looked desolate in the television series are now bursting with human activity. There are also more buildings in the city, with two great skyscrapers towering over them all. The buildings themselves are more conservative, with fewer fancy shapes and triangular tops.