I will be staying in hotels in New york and Chicago in November and I will want to do my washing! Are there any laundromats in New York near the Salisbury hotel - it's on 57th Street between 6th and 7th Avenues.
I'm at the Fairmont hotel in Chicago on North Columbus Drive, so are there any near here as well?

Ask the doorman or the front desk at the Salisbury. It is just as cheap to have your laundry sent out. The cost is by the pound.

Midtown Manhattan is primarily a business district - and I doubt you will find many laundromats. And even in the residential areas of Manhattan - it;'s mostly drop off in the am and they deliver back to you. (If you mean a place where you can go in and do your own - I haven;t seen one of those in eons.)

I used one a few years ago around Madison Avenue and 30th Street. I don't recall the exact location, but I found it here on Fodors Travel Talk.

Therefore, I think there are some self serve laundromats in the city, but you might have to travel a ways to get to one.

Yes, drop-off is the most common arrangement for Manhattanites who aren't lucky enough to have laundry equipment in their buliding. But if you have anything delicate, or things that can't survive being put in a hot dryer, you should leave them home or wash them by hand, because the by-the-pound system doesn't allow for much personalized attention.

There are a number of regular laundromats along 9th Avenue in the upper 40's, in fact, as I recall there are two in one block --45th to 46th!
They'll also do the drop off and pick up thing for a little more money, but don't expect them to take the things out of the dryer and nicely fold them before getting wrinkled. If like me, you like to have some shirts and pants (not ironed) that fold nicely straight from the dryer, you'll need to do them yourself.