I did a day tip to Malmo (Sweden) last year (2p return, +taxes, with Ryanair from Stansted). From the few hours I spent there, it was obvious that Malmo would be a great place from which to explore that part of Sweden. However, I decided to hop on the train for the short journey over the Oresund Bridge to Copenhagen (Denmark). I loved the city, but more importantly, I picked up loads of brochures about the area which really made me want to go back to explore the local towns, countryside and beaches. I'm definitely going back (hopefully for a longer visit) later this year.
If this sounds interesting to you (and if you happen to live within range of Stansted), I've just checked the prices (based on the assumption that '4 days at Easter' means out on Good Friday and back on Easter Monday). Current fares are �3.79, +taxes, each way. From Malmo Airport you can take the express bus into Malmo town centre. This stops outside the rail station and tourist information office. (The bus costs about �6, and the train to Copenhagen is about �8). Alternatively, there's a direct, fast coach from Malmo Airport to Copenhagen for a tenner. (This stops just around the corner from the rail station, tourist information office and the Tivoli gardens).
I enjoyed a two-city (indeed, two-country) break in a day at a fairly relaxed pace. With four days you could have a really great mini-holiday. Both Malmo and Copenhagen cater for tourists without being 'touristy' and you'll be spoilt for places to eat and to explore.
Chris