Curiously, traveling in Spain is quite expensive though your student card gives discounts. You can also organize a one-day-trip to the other small cities of Valencian Community like Gandìa, Castellò, Sagunto, Xativa or to the Albufera Natural Park.
If you have the tarjeta jove, you can only get a discount if you are below 26 years old.
To go to Ibiza
You can choose to go by plane or by boat, remember that prices are higher for tourists. Anyway, this trip will cost you money. Get some information from former Erasmus students because there are great chances that trips will be organized by students of your university.
But you can also compare prices before booking, bear in mind that booking in advance can help you to save a few euros.