Theoretically, you can meet intelligent women almost anywhere: every demographic has its share of smart people, from MENSA meetings to NASCAR races.
If you're a smart guy and want to find a woman who matches your intelligence level, however, you may want to focus on places which tend to attract smart women. Specifics vary depending upon your locale, but some general guidelines may help point you in the right direction.
Museums and art galleries tend to attract bright people.
They provide quiet atmospheres -- giving space for contemplation -- and their pieces serve as fuel for perceptive and creative minds. They also provide good discussion fodder at the coffee shop afterward. It helps to know what you're talking about before approaching a woman at a museum. Read up on art history and have some idea of the movement which the various pieces embody, as well as particulars about the artists themselves. Many museums also have volunteer programs for those who would like to lead tours or provide symposiums on the collections. Signing up for such a program provides a great fulcrum for spending time with like-minded women.
Bookstores and libraries may seem like a no-brainer -- and to be sure, not everyone attracted to the latest bestselling potboiler is bright -- but if a woman is intelligent, chances are she likes to read.
School libraries work well too, since they attract women attending classes on campus. Many bookstores encourage casual browsing and have comfy chairs for curling up with a book. Many others have coffee shops attached, where people can read or surf the web over a cup of java. Both of them permit lengthy stays, allowing you to hang out and get acquainted. Libraries and bookstores may also host events like reading groups, providing an opportunity to interact with women in a more structured setting.
Comic Book Conventions and Sci-Fi Gatherings
"Geek" snickering aside, fantasy and science fiction have always attracted smart people.
And while the ranks of fandom have traditionally been male, those demographics have shifted in recent years. Checking out a local comic book or sci-fi convention may help you to find girls interested in the brainier side of pop culture. Watching and loving the same show as a given girl, reading the same set of books, or going to the same movies provides an instant point of commonality to discuss. Most conventions have tons of events as well -- symposiums and guest speakers talking about the latest pop culture fad -- giving you something to do together once the casual chatting is done.