There are some possible accomodations for your trip.

Urban Life Budget Hostel
1081 Budapest, Népszínház utca 31.
2.125-2.660 Ft/person/night (in a room for 8 or 4 people, with shared bathroom)
Traveling to the competition: Metro 4: 15 minutes (from II. János Pál pápa tér - to Szent Gellért tér)

Hello Budapest Hostel
1093 Budapest, Gönczy Pál u. 1
2.820 Ft/1 /person/night (in a room for 4 or 10 people, with shared bathroom)
Traveling to the competition: 10 minutes walk or Tram 47/48/49: 8 minutes (from Fővám tér - to Szent Gellért tér)

Hunguest Hotel Platanus***
1087 Budapest, Könyves Kálmán krt. 44
10.000 Ft/2 people/night (in a room for 2 people with bathroom)
Traveling to the competition: Metro 3: 30 minutes (from Népliget - to Kálvin tér)