GödöllŠis close enough to Budapest that you probably won't need to look for accommodation here. If you plan on staying, however, here are some options.
Panzió Sissi Dózsa György út 36, (http://www.panziosissi.hu). Free wifi internet access. A little bit north of downtown. The Pizza Max Cafe is on the first floor.
Galéria Restaurant and Pension Szabadság tér 8. Reasonable prices and a central location. Also has a traditional Hungarian restaurant.