Generally, rent can be quite expensive throughout Amsterdam. You have to pick either a great location or cheaper rent.
Amsterdam is not a huge city and with its tram, bus and metro network it's quick and easy to get around. So even if you live outside of Amsterdam city center, you can go to all the cool places quite quickly. From my experience, 20-30 minutes from where you live to a great nightclub / bar / cinema / shopping / touristic area is normal if you live in a cheaper rental area (outside of Amsterdam city center).
There is no one great area for students (that I know of), however all around the outskirts of Amsterdam you can find great deals to share apartments with other international / Dutch people / students or maybe even rent a place of your own.
I suggest doing some online research to shared housing and cheap apartments in north Amsterdam, south-east and also west (pretty much all around).
I am not a student myself, but have plenty of experience looking for affordable accommodation around Amsterdam.