sumersolt
I think that with a much younger girl you'll probably have more "understanding" problems. Young girls are mostly drama. They haven't experienced mature love and they don't really know yet what they want, so unless you really think she's worth it, you probably should give up on this one.
I have lots of friends who are "too busy" to have fun, to go out, to meet people. What they're doing is they're putting their live's on hold. We're all in this rat race to a certain degree, but we shouldn't forget what's important (unless you've decided that your work is more important than meeting someone who you might end up spending the rest of your life with - which is ok with some people, since they made that decision). But I'm assuming you do want to meet people since you've posted here, well some suggestions for meeting places: coffee shops, libraries, book stores, museums. And don't think twice about approaching a girl, just do it. The worst that can happen is that she'll be rude or say no. In that case you should be glad you didn't waste your time. With time it will become very easy to approach girls. Have fun, and don't work too hard - let us know how things are going :)