Hi,
Is your budget $10 a day? Anyway, I'd advice you to get hold of a current Kenya lonely planet and check out some of the offers they have there. While I'll try not to sound too patronizing, avoid help offered too easily especially from people expecting anything in return. Meanwhile, try to get in touch with other people from your country already in Nairobi who might be able to advice you on sharing appartments and such.. And check out lonelyplanet thorn tree.. that always has many more ideas..