Use the internet to watch performances
While nothing beats watching a performance live at Lincoln Center or the Palais Garnier, you can find many incredible performances online whether through YouTube, Netflix, Hulu, or other services. Oftentimes, you can find full-length ballet, symphony, and opera performances on YouTube---including vintage performances from cultural icons. Netflix and Hulu feature wonderful cultural documentaries.
About anything. Purchase coffee table books from the bookstore and borrow library books about all kinds of cultural outlets. Some great options are Poetics of Music in the Form of Six Lessons by Stravinsky or the new book about Hamilton.
Listen to cultural podcasts
This is one of the easiest ways to absorb cultural knowledge from anywhere in the world. Some recommendations are SymphonyCast, The Dinner Party Download, and anything from The New Yorker.
Visit a local performance venue
You may not have considered it, but why not patron your local venues? Just about every town has a playhouse or theater which host local and traveling performances. It may not be Broadway, but there is nothing like a live performance. This is especially important for children. I can guess with confidence that my love for culture stems directly from the fact that I attended many, many plays as a child.
Take advantage of culture when you travel
Of course, the best way to experience the best cultural attractions the world has to offer is to visit them in person. Whenever I visit a major city, I make a point to attend some sort of performance (although it usually ends up being ballet). The next time you go to New York, Paris, London, wherever---be sure to pick up tickets for a good play, symphony, opera or ballet and take advantage of being within the vicinity of some of the world's most talented performers.