This is a review I don't want to write. Tokyo ESP should have some reason I can recommend it. Well it has nice art (inconsitently), and a sort of okay protagonist. Past that this quickly collapses into a pile of.. stuff? I'm not sure what this anime is trying to do. This review will have spoilers, which won't even be at the top of the list of things you'll have to endure if you decide to watch this anyway.
Tokyo ESP is a creation by the same guy who did [ga-rei-zero|Ga Rei], which has an anime adaptation I loved. I suppose the anime studio was thinking the same thing when they put much of the finaly in the first two episodes. There is lots of action which helps, but it doesn't have that sense of mystery which worked so well for Ga-Rei. This means the anime will end up rehashing this stuff later on, which in turn means it has less time to flesh out the "story", and it front loads the anime so it becomes less climatic later on. These problems aren't obvious at first, but it becomes painfully so in hindsight.