That depends on what methods of transport are available in the city. Historically, cities only generally saw sudden surges in size when new kinds of transport became available (ie: coach, tram, subway, car). If 99% of the population are walking to and from places in the city, it's going to be small regardless of how wealthy it is. A city a mile wide would be considered big. For example, remember that people need to eat so will have to buy food to prepare, or travel to somewhere that serves it (not everyone had kitchens). Having to walk ten or even five miles to the market and back just for food is not ideal.

But if it's a wizardy city, there could be easily available magical transport whether that be magical vehicles or fixed magic gates providing instant movement from one spot to the next. In that case, it could get really huge.

With regards to your public square, again, it depends what it's purpose is. But it'll generally be pretty large if it's used for markets or public announcements.