Mice tend to stay away if they smell cats, but if you really want to be free of them, buy a ferret!!!!
My brothe-in-law had one in his student digs, and his room, the adjacent rooms, even the kitchen (he always took Polly when he went there to cook or wash up) and the fusion (common lounge) were free of mice. The place was an old monastry and it was riddled with mice, but not where Polly roamed.
They had a cat, one floor below, and they had their relatively mice-free zone as well, but the cat wast not nearly as efficient in scaring them away as Polly the ferret.
But if you have good hunters, it will help. Jiskefet even cleared the riverbank near our house of rats. No rat to be found for the 2 years he reigned over teh area. Within 2 months after his death, there were rats once again.
And we never had to worry about moles in our garden when we had Tuppence and Jiskefet, either. They were both mole hunters. Just killed them for sport, they didn't eat them.