Been to a few countries without ever visiting the airport - Monaco, Liechtenstein and the Vatican are a given, but also Slovakia, Slovenia, Bosnia, Pakistan, Estonia, Lithuania.

Otherwise, been to a few capital cities without using their airports (some overlap here, and I'll pass on the microstates): Bratislava, Ljubljana, Sarajevo, Islamabad, Tallinn, Vilnius, Canberra, Wellington, Rabat.

Otherwise, major cities? Venice, Valencia, Cologne, Stuttgart, Krakow, St Petersburg, Samarkand, Lahore, Peshawar, Kyoto, Hiroshima, Amritsar, Adelaide, Melbourne, Brisbane, Fes... I guess some of these aren't so rare.

Some asymmetric flights - I've only ever departed from SFO and SEN, and I've only ever arrived at NWI and BHX. Several times for each.

HYD is an odd one. Arrived many times internationally (from LHR or DOH) but only ever left domestically (DEL, CCU, MAA).