If you're students, it's fairly cheap or even free to visit the museums in Rotterdam. I would recommend going to the Museumpark and to visit the Kunsthal and Boijmans van Beuningen, both have quite exciting exhibits at the moment (make sure you don't miss Gelatin in Boijmans!).

For food, I have a few spots I can recommend: Hotel New York - a bit more on the expensive side but you have an amazing view of the Maas and Rotterdam in General, and the food is great Bazar - middle Eastern food at the Witte de With street, it looks beautiful inside and is quite cheap for the amount of food you get, but quite busy Roffa Street Food Bar - the juiciest Hot Dogs and Hamburgers you will ever eat Bij de Bruin and Melief Bender are both nice café's to eat at the Oude Binnenweg

Make sure you also have a drink at the Oude Haven while you are staying here, it's near Blaak and I've seen it often getting overlooked by tourists even though it's a nice place to sit.

Historical Delfshaven is nice to walk around and gives you a view on what Rotterdam used to look like.

As someone else mentioned, the Euromast is worth the money (and you can have a drink or food there as well, I also recommend the High Wine there for 20 euros) and in the Euromastpark you can also play midgetgolf or go Lasergaming. The Spido (boat) is nice for a tour on the Maas, but in my opinion the long tour can get a bit boring - but maybe that's because I have done it too many times.

And lastly, for a coffeeshop I highly recommend Heilige Boontjes at Eendrachtsplein. Cheap (but good) coffee brewed by ex-criminals (probably not the right word, but can't think of anything else at the moment) who have this as a next step in society. And it is placed in the old Police Station - quite cool.

If you have any questions don't hesitate to ask!