I'll add my support to Barcelona. Spudqueen has mentioned travelling via Reus but you should also check out the flights to Girona. (There's a direct bus to Barcelona from there as well). On some dates, flights to one of these airports can be far cheaper than to the other one.
I enjoyed a day trip to Malmo with Ryanair. I spent a few hours looking around the city and then hopped on a train to Copenhagen. (The trains are fairly cheap. They run 24 hours per day, with departures every 20 minutes for most of the day).
If you decided to skip Malmo and go straight to Copenhagen, there's a direct bus from Malmo airport.
I've done day trips to Genoa several times. The timetables have been changed, so day trips are no longer possible but you might be able to fit in a short break. (There's a good, cheap bus service from the airport to the city). The old city of Genoa is fascinating but the real attraction is to take one of the incredibly cheap trains along the coast to the delightful resorts of the Italian Riviera, such as Rapallo and Santa Margherita.
Chris