I am looking at airplane ticket options from Chicago to Geneva. One option gives a 5 1/2 hour layover in Schiphol starting at 7 am. If I left the airport to do some sightseeing, how much time would I actually have, taking into account going through customs and checking back into the airport?
If you decide not to leave the airport, there is a branch of the Rijksmuseum inside Schiphol.
You have time for a quick visit, but at that hour not much is going to be open. But if you're looking to just stretch your legs and/or do breakfast, it's doable. It should take no more than an hour to exit the airport, and the train journey is 15 minutes. If you already have your boarding pass for your connecting flight head back to the airport 90 minutes before departure. If you need a pass allow 2 hours.
The Museum is in teh secure area, so make sure you see it before you go into teh main public part of the airport or after you have cleared security. We got caught with this. We were arriving in Schipol andtravelling onward teh next day by train. We thought we could see teh museumbefore we caught the train, but were out of luck.
The train station abuts the airport. Make sure you have Euros when you leave the airport - once you are in the train station $$ are useless. If you are into Van Gogh, you should be able to get to "his" museum for a couple of hours. Or buy a "walking tour" pamphlet at the tourist office (should be one in or right outside the Amsterdam station) and go exploring.
BTW I doubt it will take you as long as an hour to get out of the airport. If you have a lot of carryon, you can store it in a locker in the airport. You will need coins.
Amsterdam is a really efficient airport, you can get out of there really fast and then it's a really quick and easy ride into the city centre. Only exception: if you can't check your luggage through to Geneva and have to pick it up in Amsterdam to re-check it, that could easily eat up a lot of time. Luggage retrieval is one of the few weak points of Schiphol.
You should have plenty of time to have breakfast, walk along the canals, and explore maybe one museum if that's what you're interested in. The Anne Frank Huis and the Rijksmuseum open at 9am and you can buy tickets online from home before you leave, thus eliminating standing in line and loosing time that way (school classes line up in front of Anne Frank quite frequently). The Van Gogh Museum opens at 10 am. Personally, with limited time I'd skip the Rijksmuseum, it's too big, and choose one of the other famous ones.
Lockers are a bit of a problem. Schipol has lockers but when you arrive at the airport from a transatlantic flight,you enter the non-schengen half of the terminal. Problem is when you reenter the terminal after your excursion in Amsterdam you will enter the schengen half of the terminal where the flight to Geneva departs from. So they only way to get to the lockers again is to pass through the immigration check between the two halves of the terminal; that means two lines. Thus it's easier to use the luggage hold in the Schipol Mall portion of the airport. I don't think going to one of the big museums like Van Gough is a good idea on such a short layover. It's not within walking distance from Centraal Station, so you're going to have to deal with trams or taxis to get there. Also, you're going to feel a bit rushed and won't be able to appreciate the art work. Better to save it for a proper trip.
Michael has a good point. I used the luggage hold as well after arriving from Canada. It was a bit difficult to find but it still left us enough time to take the train to Amsterdam Centraal and explore a bit of the city.
From the train station (do not miss the huge parking garage for bikes!) we walked to the Anne Frank Huis. The walk takes usually 15-20 minutes and we really appreciated it after the long journey to Europe, especially considering the really pretty surroundings. So in our case the walk took a few minutes longer since we stopped here and there to take pictures. We stood in line to get into the Anne Frank Huis for half an hour (at the time online booking was not possible), toured the museum for about an hour. This is a very small place, just remember the feelings of claustophobia Anne described in her diary! So even with the adjacent museum it is not a huge place that takes hours to see. After that we had coffee at a small canal-side cafe. Walked to the train station and got back to the luggage hold less than 4 hours after our plane had arrived.