Our flight was just changed having us spend a day in Lisbon. We land at 2 PM, will stay at an airport hotel and fly out at 11 AM the next morning. What would you do with a single day in Lisbon?
The airport is near downtown so stay in the city.
You may not have as much time as you would like. If you are arriving from a Schengen country passport control can be pretty quick. We flew from London and waited 4 hours-a nightmare. Assuming you avoid that, Suki is right, stay in town. The airport is only a few miles from the city center. If you taxi, do not join the long line but go upstairs to departures and just grab a cab dropping off passengers. Or Uber, which works very well in Portugal. We stayed at the Hotel Lisboa Plaza on our recent RS tour. It's well located, has a very good breakfast. Behind it is a weirdly situated very casual restaurant, A Gina which has very good seafood and grilled meats for a reasonable price. By the time you get to your hotel you won't really have much time except to wander around.
You might want to book a taxi ahead of time. That would save standing in the long taxi line. Lisbontaxis.com does a great job. You email them for a quote and they are waiting for you when you arrive. If you stay in some of the main tourist areas, you can also take the Aerobus. It's cheaper but there would still be some waiting involved. Also, if you are traveling after the summer rush, the waiting times at the airport should be better.
If you stay in the Baixa, Chiado or Rossio áreas, you will be close enough to walk around and see a bit of Lisbon and have a nice dinner. If it's before the time change, you should still have several hours before dark. If you google 'miradouros Lisbon', you will find a number of places to really view of beauty of the city.
go into downtown, wander around the historic neighborhoods, have a great seafood dinner, catch a fado show