The Pokemon anime is a bit off-balance, and it's always the same thing. It gets boring after a while (plus there's several hundred episodes you need to get through) but I would recommend Origins, there's only 4 episodes but it's worth reliving the RBY moments if you played the series.
If not, I've heard Steins Gate is good. One of my friends loves anime, and she likes No Game, No Life (or something like that). I have no idea what it is, I'm pretty sure she said something about it being like a virtual reality thing (I'm definitely getting this mixed up with another anime she talks about) but I'm not sure.
A couple other animes I've heard her talk about
Sword Art Online (I think, might just be Sword Online)
Naruto (everyone knows what that is)
And that's all I remember. I'm sure she said more but I have horrible memory.