I have only taken the averages for rentals that closed in November.
For all closed rentals the average is $5.67/ SqFt and this is for an apartment that has about 3.5 rooms, so anywhere from 1BR to 2 BR. I have to agree with Anna that the averages will change depending on what you're looking for, in addition to the variables that Anna listed, the average $/SqFt will also change depending on the services a building offers as these are funneled back to the renter through the landlord, even though the landlord pays for them directly.
Please let me know if you have a specific building in mind, because then you can look within the building what the average $/SqFt is (approximately) because even in a building the average $/SqFT changes depending on the location within the building and for example a view or not and of course on the condition of the apartment. So this average is a very general guideline as two apartments in the same building and even of the same size can have a total different $/SqFt average.
Representative, Licensed Real Estate Salesperson