Housing in Zealand is an interesting choice due to low transport time from Roskilde and Køge to the capital. The costs are definitely lower on the rental offers and you can possibly save up to 25% compared to Copenhagen.
It is a good choice to locate to a place in Zealand, especially if you are looking for a quiet place, and want to live in a smaller city of approximately 40-50 000 people. There are benefits such as easier access to a place to stay and lower prices as well. Roskilde is cheaper than Copenhagen, and you will approximately be able to save around 25% on rental offers. In case you already have a contract before moving, you could ask the company to help you out to make your life easier on the housing situation. Another typical approach is to ask friends of friends on facebook for help to find a room or apartment.
Sources:
Expatistan.com
Boligsurf.dk
Findroommate.dk