DH and I often travel in off season.
Sicily- Palermo, Agrigento, Catania. We did a mix of train and buses. I've heard Cefalu is lovely, but its a beach resort so might be the wrong time of year.
Malaga- Not the beach resorts along the coast, but Malga 'city' itself. Less touristy, great good, some museums, hugh fruit/veg maket etc. A lovely day trip via train is Ronda. It has a historic and famous bridge and some of the restaurants are amazing.
Crete- We stayed in Reythymon which had some smaller museums but an interesting fort and things to see. Food was nice, but not as varied as Italy or Malaga. We caught a bus and went to Heraklion to see the Knossos site. The museum in Heraklion was really good.
Budapest- We went in Dec. A day at the Gellert spa was amazing. The parliament building- book tickets before you go because it can book up quickly. Museums, the basilica, large synagogue and alot of history. As part of the Austro-Hungarian empire, they had some amazing pastries to rival anywhere.
Prague- This was 15yrs ago, but the food was far more meat based, dumplings and veg only when ordered. Still loved it though. Wenceslas square, the clock etc. There is Sedlec ossuary has a half day trip via train- a unique church/museum of bones! Also Cesky Krumlov is stunning and also accessible from Prague.