I Love anime. Really. That, right there, is my life.
Anyways, some anime, like Naruto and Bleach, aren't too easy to get into. I personally believe they both went on for far too long and have no desire to get into their fandoms.
However, some anime have quite...interesting plots. I will admit, though, a lot of them do involve Japanese school girls in very short skirts.
However, some are filled with extremely intellectual plots. Such as Death Note. You know who Kira is, and it's all about whether you want Kira to succeed, or the police force, and from there, you watch them spin long, intricate webs abound each other.
And not all anime is childish. Death Note certainly isn't. Those character's even creeped me out, and I'm in high school...but I digress.
I honestly think you should give anime another shot. I personally don't think you should start off with something so out there, repetitive, or, well, obvious as fandoms such as Naruto and Bleach. And that also includes Full Metal Alchemist, so I'm very sorry to anyone from those fandoms if I've offended you, no harm meant from my statement.
Perhaps try something a bit more...you. What kinds of things, genres, are you into? If you want something a bit more intellectual and less on relationships, and don't mind some creepy/gruesome/well, death-filled things, I highly recommend Death Note. It's short, only about 37 episodes, but it keeps you interested. However, I will give you fair warning now...don't get attached to characters if you begin to like it.
There's also a lot of comedy anime (Such as Hetalia Axis Powers, each episode is only five minutes long, and since it's based on history, there are a lot of, somewhat accurate, historical happenings, i.e., the Seven Years War, the Opium War, the Revolutionary War...), there's harem and reverse harem anime, there are sci-fi, fantasy, supernatural, adventure....there are so many out there, but you need to find something that appeals to you. For instance, I like either a lot of comedy in something, or some kind of dark, or fantasy like setting. Supernatural stuff is my forte, but you need to make sure you don't just try something randomly. If you want, without getting spoilers, look up the anime, figure out the genres, how long it is, and get a quick summary, but no plot details. Just don't give up to easily, because you'll never know unless you try, and I know for a fact, it sucks to like anime and not have anyone to share your opinions with. So its one of those things you always need an open mind for.
Good luck, and I hope I at least somewhat helped you!