You may find accommodation on one of the following sites. There are plenty of apartments for rent at a reasonable price.
If you need any help concerning the reservation, please contact the organizers.
You will have to use public transport to get from your hotel/hostel to ELTE.
The Budapest public transport company (BKK) sells 7-day travelcard for 4.950HUF (~13EUR).
Don’t forget to bring your student id, because EU students may buy a monthly Budapest pass for 3.450HUF (~9EUR). Your student id will also entitle you to reduced entrance fees at museums etc.
More information at the website of BKK.