Living in Central Denmark is a good choice, especially if you want to live in a modern cultural capital, which in general is 20% cheaper than Copenhagen if you consider the housing market and also has less competition on the labor market. The competition to get a place to stay is not as high as in Copenhagen and Aarhus is a cozy town.
Finding a place to stay in Central Denmark in Aarhus is not an easy task, but much easier than finding something in Copenhagen. You will have many benefits by living in Aarhus. You can save 20% in general on your housing. There is variation between the prices of flats near the water, central city and 30 minutes outside the city center. Housing in Aarhus will give you benefits of easier access to a social life and a connection to the locals and other expats compared to smaller cities in the region.
Sources:
Expatistan.com - comparison of house costs
Findaroommate.dk - Find your roommate
dba.dk (Danish platform for sales, renting etc.)