The word you are looking for is "aneks kuchenny" (a small kitchen, usually being a part of another room).
From what I understand (and looking at Google Graphics), a hob is only the top part of a stove.
Oh hang on, so a stove is including the oven? I thought they called ovens ovens. Ah now I think about it, I seem to remember hearing the word 'stovetop' at some point, so that must be what they call a hob, and then the oven is the other part of their 'stove'. Ok. So back to Polish, the kuchenka is the whole thing, oven plus hob, is that what you're saying? And oven is piekarnika, right? So what's a hob called?
"pieca" is Genitive, the basic form is "piec".
Geez, I don't know, I think it would be best to use Google Graphics... frankly, I remember having doubts about accepting "piec". Oh, rather google "piec kuchenny" for it, otherwise the results will be too different.