Yes, Barnard will fit many of your criteria. For one, they do have a strong English and Psychology department.
Then, NYC, with its many performing venues/clubs, TV studios, theatres, etc. does offer up a breadth of opportunities hard to match elsewhere. (If I remember correctly, both Cynthia Nixon, and Suzanne Vega took the train downtown after classes, because they had gigs).
On the other hand, serving the Manhattan population are many hospitals, other universities, clinics, and private practices, that offer internship opportunities in the Neurosciences, Psychology, etc.
And Barnard/Columbia have an active student music/performance/production scene, with various clubs, publications (e.g. http://www.ratrockmagazine.com/), etc.