I have never been to New York, either the city or the state, and live in the Chicagoland area. Chicago itself, outside the downtown area, looks much like the older suburbs, with bungalows, two-story (usually) commercial buildings, etc. So how does New York City compare to Chicago, especially with older buildings?

Can't say there is much in the way of two-story anything in Manhattan itself. You will find smaller residences in the other four boroughs, but NYC proper is lots of skyscrapers and tall office buildings. For example, on the Upper east Side I lived in a 5-story pre-war building, but I was surrounded by several apartment buildings in the 15+ story range. The Wall Street area is like rafting down a narrow canyon, i.e. the streets are kind of narrow and walled in by tall office buildings giving a very closed-in feeling. Manhattan is built on a long, narrow island which prevents it from spreading horizontally unlike Chicago which is able to spread out.

Here is an aerial view of the Wall Street area (pardon the smoke, my work place had fallen down a few days earlier):


Here's a more recent view from my mother-in-law's 19th floor apartment balcony along the East River looking south towards WS:

Great views! I'm glad you weren't at your workplace on 9/11.
Engineers (Middle Easterners I think) are just about to make raising buildings a mile high and even taller practicable they say, so maybe the city will be able to expand upwards rather than outwards. Something surely has to be done, to increase the density of the city so it stays (comparatively) affordable.

Actually, I was standing on the street outside Building 5 discussing what to do with my coworkers when the second plane hit. Running from the falling debris is what saved me when it collapsed, but just barely. An avalanche of dust is hard to run from, even with a block-long head start.