While it's nice to be able to enroll kids in classes or hire tutors, city homeschooling really can be done cheaply given all the free and low-cost offerings the city provides. In addition to our public libraries, most cities are fortunate to host world-class colleges and universities that offer an astonishing array of lectures and cultural events that are often free and open to the general public. For example, this week alone at Harvard you could hear a free lecture on the constitutionality of Obama's healthcare reform or participate in an African Dance Diaspora symposium, while at MIT you could participate in a free and open lecture on nuclear and particle theory. Just check out the event listing website for your local college or university to see which programs are free and available to you.
Many museums are also free and open to the public on certain days of the week. Here in Boston, for instance, the Museum of Fine Arts offers free admission every Wednesday afternoon after 4:00, the Institute of Contemporary Art offers free admission every Thursday evening, and the MIT Museum and the Harvard Natural History Museum both offer free admission on Sunday mornings.
Combine all of the above with each city's frequent cultural events and festivals, local bookstore lectures, poetry readings, and musical street performers, and you have a robust homeschool curriculum for very little cost -- with affordable public transportation to access your city's many educational offerings.