The cheapest shops where you can buy food are called Netto, Rema1000, Lidl, Aldi, Kiwi and Fakta. Many stores are open everyday from 8 am to 10 pm.
They are many places around town, and easy to find otherwise simply ask a passerby.
Go for these signs:
Other grocery stores in the center of Aalborg is Føtex, Kvickly and Superbest. Go for these signs: