Helsingborg

Kullaberg/Mölle
is an easy day trip and a must in late Spring/Summer. Kullaberg national reserve offers nature trails with great views over Öresund and the surrounding countryside. Take regional yellow bus 220 towards Höganäs Mölle.
Denmark
Elsinore Helsingör is easily accessible by ferry 20 minutes. For Humlebæk and Copenhagen take a ferry to Elsinore, then a train. Ticket for the whole trip one way or return can be bought at the Ferry ticket window.
Lund
the University town 40,000+ students of south Sweden and one of the oldest and most historic towns in Sweden.
Malmö
is Sweden's third most populous city ~300,000 people and the main Swedish city of the region.

For Lund and Malmö, take a local train Öresundståg.

It's possible to take a train all the way to Kastrup/Copenhagen via Malmö, which is convenient if you have luggage, but it takes a little longer and costs a little more. Most trains have Malmö as final destination, so make sure yours goes all the way.