Bankrate.com reports that you can cancel any policy when needed:
Auto insurance companies generally give you the right to cancel your policy at any time, as long as you give proper notice. Typically, your entire unused premium will be refunded, though some insurance companies will charge a small fee if you cancel in the middle of the policy term.
Difficult to locate companies since most ask for a 6 month policy to begin with. I have though found some companies that you can look into for coverage:
In terms of the 5 cheapest insurance companies in NYC:
1. Progressive shows up in many listings in various listing
2. Geico the same
4. State Farm
5. New York Mutual