in NYC there is no right on red, it's not allowed. there's a space between the cars going straight and the crosswalk that cyclists can move into. they are directly in front of cars going straight and have right of way once the light turns green. in general, we try not to get left hooked or right hooked, there's a "mixing zone" we share with cars to avoid that. but if the lane is on the right, there is usually no safe place to move - no car has ever asked me to move and if they did i would probably say no, there's typically no safe way of executing such a move. they usually yield and wait for me to go before making their right turn. hope this helps clarify what happens in NYC.