The World God Only Knows
Keima Katsuragi, a second-year high school student, is an avid dating sim gamer. He is known on the Internet as "The Capturing God" for his legendary skills to be able to "capture" any 2D girl in games. However, in his actual school life, Keima is known as otamegane, a derogatory portmanteau of the two words otaku (オタク) and megane (メガネ-"glasses").
At the start of the series, Keima receives an e-mail offering him a contract to "capture" girls. He accepts what is thought to be a challenge, and a demon from Hell nicknamed Elsie appears. She asks for his cooperation to help her in catching the runaway spirits. These spirits hide themselves inside the girl's heart, and Elsie suggests that the only method to force the spirits out is by "capturing" their hearts—making them fall in love. Appalled by the idea, Keima refuses after clarifying to Elsie that he is only interested in "capturing" 2D girls and that he detests reality. Nevertheless, with the contract already accepted, Keima would have to help Elsie no matter what; if they fail, both Elsie and Keima would lose their heads.
First season is completed with 12 episodes and Second season follows again with 12 episodes. I found this a very good anime to watch, it has a lot of humor mixed into it and it is very fun (for me atleast) to watch how Keima puts his gaming expierience to test in the reality world and see how he conquers real girls instead.
I have been trying the exact same thing but i think you can't find an anime that you will love the first season, you actually need to have interest and watch atleast a few. Maybe the anime i suggested above might work out for your girlfriend, thing is with that anime, there are no fillers as in excessive conversations, so many things happen in a single episode that are relevant. Try the first episode and see what i mean and maybe recommend it to your girlfriend
Heres the OP if you might be interested: