Oops you're right. I must have misheard. Thanks Tori.で is the correct answer for an exercise in Genki I Chapter 11 Practice Ⅱ A-2 "きょうこ: made sweets, played games at home, etc." since 家 is the location where the action takes place. Where did you get the answer に?
Both are correct. は is the topicalized version of に, so you can also use お昼ごはんには、なにが食べたいですか as well. This は or には can have a contrastive nuance, something like "especially as lunch, not breakfast or dinner", whereas に is neutral.