The age limit varies from venue to venue. In general you have to be older than 18 years to enter any nightclub. But most places have higher age limits on the weekend. Most of the time you are safe when you are 21 and older, but sometimes you will also see 23+.
Please make sure to always bring your ID since some places (especially nightclubs) actually check upon arrival.
Since we know the struggle, we try to make sure and inform the venues that at the events we promote the age limit is always 18+ so that you and all your fellow exchange students have a chance to go out together!