I've only ridden it once, but I think your best option would be to ride the airport link train into the city and then stay at a place that is very near to the airport link station. You can walk around the area that evening, eat dinner, sleep, then wake up early and take the train back to the airport. I'm not sure what time the first train runs to the airport though.

You're not going to "walk somewhere local out of the hotel" if you stay at the airport hotel.