hi jojo, playa de las americas in tenerife is only 20 mins in a taxi from the airport, or, depending on the driver, maybe 15, ha !

Sharm airport to the Conrad hotel, ten minutes.

Pippy

Ibiza, Playa D'en Bossa, 10-15 minutes
Infact anywhere in Ibiza is an hour at the most!

Dalyan in Turkey is only 1/2 hour from Dalaman airport.

looking into this myself and came up with Rimini, Italy which has its own airport and Lido de jesalo not far from Venice. Palma Nova near Palma, Majorca and I think there are a few places to stay near to Faro airport on the Algarve.

puerto del carmen .lanzarote ,15 mins away

Arrecife in Lanzarote, approx 10 minutes. Los Cristianos-Tenerife approx 15 minutes

Ibiza, Playa d'en bossa, 10 mins
Salou, Costa Dorada, 10/15mins.
Palma Nova, Majorca, 15/20mins. In our experience.

Costa Caleta de Fuste in Fuerteventura is so close to the airport you can pretty much see the runway as you're on the main road from the resort back to the airport! We stayed there this Easter and it was fantastic for plane-spotters - the planes come very low over the resort although you soon get used to them and there are no flights to disturb you in the small hours The coach transfer with the tour operator was about 10 minutes, it would easily be less than that in a taxi.

Also, as others have suggested:
Puerto del Carmen/Matagorda in Lanzarote. Costa Teguise is quite close as well.
Los Cristianos/Playa de las Americas in Tenerife.
Palma Nova/Magaluf in Majorca.
Playa d'en Bossa in Ibiza.

I think there may be one or two Greek islands with resorts close to the airport too.

thank you now to find a cheap holiday website

Vilamoura in algarve = 20 mins

puerto del carmen in lanzarote = 5-10 mins, not 15 as stated

costa teguise is only 20 minutes by taxi also on lanzarote

menorca has punta prima, cala'n'porter both 15 minutes

salou on the costa dorada is 20 minutes or so

luckily there is a reasonable choice for those who don't like to be on a coach for 2 hours!

Kalamaki - Zakynthos = 10 mins
Laganas - Zakynthos = 15 mins

Puerto Del carmen in Lanzarote is the closest resort to an airport I've ever seen that doesn't suffer from aircraft noise!

Can Pastilla 5 minutes from the end of Palma Airport runway. CBG

Agree on above, also Can Pastilla runs into Playa de Palma and Arenal so any of those resorts would also be suitable for you from Palma airport.

Skanes, Monastir or Sousse from Monastir (Tunisia). The first two are about 5 - 10 minutes and Sousse about 20 - 25 minutes.