Again, the chart can also be found at http://www.alafista.com/2013/04/25/summer-2013-anime-lineup/
At the top of my maybe list is Chou Jigen Game Neptunia The Animation, the adapatation of the Playstation 3 game. I haven't played the game myself, but I have friends who did, and they seemed to like it, so it might be worth a look.
Second might be the Danganronpa yadda yadda yadda, another adaptation of a game with a pretty interesting premise, though the weird devil-bear mascot kind of throws me.
I'm also on the fence about Fantasista Doll. which looks like it might be a magical-girl Sekirei type affair. Could be good, but I withhold my judgement.
Lastly, I'm feeling maybe about Kin-iro Mosaic. Reading the premise, it's not 100% my shtick, but I was at least a little intrigued when I read it, so it may make a good watch.