which city, new york or boston, has the older pedigree in the united states?

Dear Casbrog, 

New York wins. Technically, though, "Boston", as a name for the place,
exists longer, so, if you're Bostonian, you can still have a claim to
glory.

New Amsterdam was founded in 1625, and later (1674) changed its name
to New York; Boston was founded on the 17th of September, 1630.

Wikipedia: 
New Amsterdam
<http://en.wikipedia.org/wiki/New_Amsterdam> 

Boston 
<http://en.wikipedia.org/wiki/Boston>  

I hope this answered your question. Please contact me if you need any
clarification before you rate this answer. My search terms have been
"X was founded"