rubbing isn't about the rim size itself, it's about the tire/ wheel's combo overall height, some rubber band tires have thinner sidewalls than others so using those thinner sidewall tires could allow you to use an inch or so bigger, I'd have to say that 16" or 17" would be plenty big enough though, you could probably run an inch or inch and 1/2 or so wider than the tires you have now.