Been doing it for years. Just be aware that traffic conditions vary significantly according to time. St Marks Street is empty before 7:30 AM. I can usually make most of the traffic lights from the West Side to the East with just brief stops at 8 and 7 Avenues and by running a couple of lights for small side streets on Greenwich. If you hustle you can make all the lights from 6 Ave to Ave A with just a slow down at 4 Ave. Any later and traffic becomes terrible. Delivery trucks, little kids and school buses everywhere.

There is no good route in the PM going East to West. I've seen cyclists in traffic on Delancey Street. But I have no such death wish. I've tried everything. The students around NYU have a bad habit of just stepping off the curb without looking. There is an East-West bike route on 9th Street but it is always blocked by double parked vehicles and has heavy traffic.

By going across 3rd Street and around Washington Sq there is less vehicle traffic even though there are a fair amount of traffic lights and the clueless students. By the way, this is a great route on Halloween.

Christopher Street also has a bike path but again traffic is heavy and cars are usually parked in the path. Charles street seems to have very little traffic.

Be careful out there.