If for whatever reason the main rooms of the house, like the kitchen and dining room, don’t have a Mezuzah, would it be better to light the Menorah by a bedroom or front door that do have a Mezuzah?
You should light at the entrance of the main room, even if it has no Mezuzah. Sources: לא מצינו בשום דוכתא שיש להדר להדליק בפתח שי״ב מזוזה. ומוכח…