Which day will it be? I could be in SH as well.
BTW, I did the trip to Zhoushan last year. Took the high speed boat (2.5 hours), got to the port, took a taxi to the Sheraton (12 minutes), nice, new, and probably the best hotel in town. If you fly, I guess you can pre-arrange or call to have the Sheraton pick you up for a fee.
Putuoshan is a neiboring island, and you have to pay a fee to enter (other than the boad ticket), it's 14 km away from the hotel, as said.