Great idea for a thread. Here are the airports I've visited, but not the city:
BKK (transited from SYD to LHR in 2010)
CPH (back to back in 2013)
DXB (transited from LGW to BLR and back again in 2015 on EK)
DUS (did exit the airport to get the train straight to and from CGN in 2016)
DOH (transited many times from 2016 to 2019 to and from various destinations on QR)
PHX (transited from EWR to HNL in 2017 on AA)
IAD (transited from LAX to LHR in 2017 on AA to BA)
HEL (transited from LHR to TLL and back again in 2017 on AY, although left the airport to stay at the airport Hilton)
TLL (back to back in 2017 on AY)
OSL (transited from DOH to LHR in 2018 on QR to BA and twice in both directions in 2019 - left the airport to stay at the airport Radisson Blu in 2019)
ZRH (back to back in 2018)
LIN (back to back twice in 2018)
There are more occasions where I've done back to backs or transited airports without visiting the city, but have visited the city in question at least once previously or since.