There are 14 selective collection courtyards currently operating in Budapest. These
courtyards collect both the basic stuff for recycling such as paper and plastic, and
other things such as household hazardous waste. No charge.

You can bring:

Paper: newspapers, magazines, notebooks, books, cardboard, wrapping paper
Drink cartons
Plastic: polistyrene/styrofoam (PS), PET bottles
Clear and coloured glass bottles and jars
Metal cans: aluminum and tin

Hazardous waste:
white goods: washing machines, fridges, etc.
electronic waste: computer waste and other
lightbulbs
batteries
used oil (cooking, other)

Open Monday-Friday: 10-18, Saturday: 8-14
By District...
III., Testvérhegyi út 10/a T: 439-2351
IV., Ugró Gyula sor 1-3. T: 230-2644
IV., Zichy Mihály u. - Istvántelki út corner Tel.: 370-9863
VIII., Sárkány u. 5. T: 210-5995
IX., Ecseri út 9. T: 280-6664
X., Fehér köz 2. Tel.: 260-9119
XI., Bánk bán u. 8-10. T: 464-5907
XIII., Tatai út 96. T: 329-8437
XV., Károlyi S. u. 119. T: 305-2429
XV., Zsókavár u. at the ned of the street, after #65 T: 410-5340
XVI., Csömöri út 2-4. T: 405-4584
XVII. Gyökér köz 4. T: 259-1691
XXI., Bajáki Ferenc u. 86. T: 420-7710

Source: http://www.fkf.hu/portal/page/portal/fkf/szolg/Lakossag/Hulladek/Szelektiv/Hulladekgy_udvar