Heck, Kyoto is only 35 minutes from Nagoya by bullet train. Just run over there, do the major sights and return same day. You don't even need to change hotels.

Or, change hotels to Kyoto and give yourself 2 days in and around Kyoto and Nara. Assuming you are departing Japan from Nagoya (NGO,) you can just as easily start from Kyoto to the airport as from a Nagoya hotel. Just leave 45 minutes or so earlier to allow for connection time.