Is there a place to park my bicycle At the met?

Yes, out front.

I don't see.

Yes, but without certainty because the US is rarely adapted to bicycles and pedestrians but as the museum is in front of the Metropolitan Park, it should be possible. It would take almost two days because it is huge and wonderful, I find it even more interesting than the Britisch Museum in London where the Louvre in Paris. In addition, without flash, photos are allowed and it is a more appreciated. Nice visit