If it's a wide one-way street/avenue (e.g. Third Avenue, Manhattan), don't drivers expect bikes more likely on the rightmost lane than one the leftmost lane, especially when there is a median between the two opposite one-way sides of the street/avenue (such as Park Avenue and some parts of the Broadway in Manhattan)?
First of all, I said
one way streets, though maybe I should have said Avenues.
In any case my advice applies to both, but is most specifically about the avenues. NYC used to have signs saying "bicycles keep left" on all the one way avenues. (I don't know if they still do).
It isn't so much where drivers expect bicycles, since NYC traffic is so unruly that drivers have learned to expect anything anyplace. But besides no busses, and fewer opening doors on the passenger side, riding on the left puts you closer to the driver who has better sight lines, and is better able to gauge the separation (width of his car) on his close side than far side.
This doesn't apply to Park Ave, which is a
two way street, although divided, except as you approach a left turn.
Probably the most important skill for riding in high traffic places such as NYC is the ability to hold a line. Riders who can hold a straight line consistently are more predictable to drivers and use less road than riders with less control. IMO the key to riding in NYC traffic is good bike handling skills, such as being able to look over your shoulder without veering, and confidence. One nice thing about NY is that we probably have the narrowest speed difference between cars and bikes (except that many cyclists are faster).