So is villa dative?
It is ablative singular. in with the ablative is a static, no movement to location.
The dative singular of villa is villae.
I though villa was city and domo was house??
No, villa is villa, a country house. Sometimes I translate it as house, depending on the context.
A domus is a house, smaller than a villa.
It should accept either in villa or domi. Notice there is no in with domi. It uses the older locative case.