Tokyo-3, from the subtheme Evangelion-1, is pretty much the only Tokyo-3 commonly used in IC play, and the only one readily accessed in the relevant section of the Multiverse.
Tokyo-3 has been rebuilt after Third Impact, and currently runs as it always did, except with considerable defensive upgrades should the UN try anything in the meantime - though the dead and injured were restored when Shinji Ikari reversed the effects of Instrumentality, remembering being brutally massacred is going to leave one a bit more cautious in the future. It is under the leadership of NERV, which in turn is led by Gendo Ikari, the considerably gutted SEELE also having some influence - when Gendo allows them to.
Currently the original Eva pilots, having joined the Union, could be considered as being in exile from there, though several new Eva pilots have been found, including (unsuccessful) attempts to recruit pilots from other universes (the one instance where it worked, the pilot in question escaped to the Union very quickly after her arrival).
Underneath Tokyo-3 is the elephantine Geofront, which is the center of worldwide NERV operations. It is a massive, cavernous structure, essentially a city onto itself, including considerable scientific capabilities, independent power, oxygen, water and food supplies, and even massive lighting to simulate sunlight during daytime hours. NERV headquarters serves as a large fortress, built both to withstand Angel attacks as well as more direct invasion attempts. The Geofront itself is also part of Lilith's Egg, a huge structure which was key to the Third Impact. It is not entirely clear how the Egg returned to its original position, though in all likelihood Shinji put it there when he restored the world.
Though Tokyo-3, along with its entire world, is independent and unaffiliated, it has in the past had ties to the Confederacy, and probably continues to do so out of the public eye. It is questionable, however, just how far the Confederacy is willing to let Gendo go with his plans, if they are even aware of their true extent.
This article obviously needs some expansion, which will hopefully come in time.