So I've never had a real "port call", but I have gotten to stop in Sicily and the Azores a few times.
Sicily: Stay in Catania. It'll be a little pricey, but its well worth it. That's where all of the night life is, as well as one of the main train stations, so its easy to get to most of the island from there. For sights, Mt. Etna is close, as is Taormina and Siracusa. Taormina is my second favorite, right behind Catania. If you end up in Taormina at the bottom of the hill, there are two ways to go up: cab or walk. Walking is going to be a good workout, but the views are awesome. As for Catania, aside from the bars, there is alot of good shopping and eating, as well as sights and such. Driving is not that bad, but parking is a b* and a half.
For the Azores, stay in Angra on Lajes Island. Its about a 15 minute drive from the airbase. Not as much to do as Sicily, but still fun. Lots of sights, shopping and good eating. There is a small strip of bars, but they are fairly expensive. There's also a restaurant that has "Steak on a Rock", but I can't, for the life of me, remember the name. Driving on the Azores is similar to Sicily... not bad, but good luck finding a place to park. No trains that I remember, so you'll have to rely on cabs for public transport.
I'll also put a plug in for Doha, Qatar. Nice place, good shopping. If you go, stay at the Intercontinental Hotel. There is almost always some event at the hotel. Very expensive and touristy hotel.