Manchester is in the middle of the UK 

The absolute centre of the UK is in Dunsop bridge, a little village about 1 hour north of Manchester.

If you are an international student in Manchester its easy for you to visit all the other places in the UK; Scotland, Wales and Ireland are just a short distance away. If you live anywhere else in the UK its more difficult to get to the other places. 

Liverpool is just 45 minutes away, and London is only 2 hours on the train. Manchester also has the largest International airport outside London, so it's easy to fly home.