Rebuild of Evangelion 2.22 has a bunch of scenes with TV screens. Some of them are huge screens in Tokyo where passerby are looking up at them. And the female characters Misato and Ritsuko are looking at a big screen a lot.. Not a computer monitor, but a sceen nonetheless.
My other suggestion would be Durarara!!, where there's a huge screen on a building that has snippets of another anime almost every episode. And the series basically revolves around an internet chat, so you'll find a lot of computers.
