hi Susan
lots of moving companies are located out side of Manhattan, and the reason for that is high rent, that's the reason movers are getting the licensees for NY and they are located in New Jersey for example. If they will present you the New York state local license that ok. FMC license authorize movers to move state to state regardless their position.
Regards your question about
moving companies from California: movers have large moving truck that drive from New York to California on weekly basis and they can provide you with very good estimate for your move.
I recommend you to check BBB for each moving company.
hope it helps
Dan