London did this a while ago and traveling around the city is much more pleasant. There is a case to be made that a congestion charge makes a city more habitable.
The way London does it does create some asymmetries which would be good to avoid. You pay when crossing the border between the outside and the congestion charge zone while driving inside the zone is not charged. This means that those who live inside the zone and drive inside the zone don't pay while those who come from the outside do. London real estate being priced as it is, those who live inside the zone could easily afford to pay for the privilege of driving private vehicles in that area - but they don't. Those who can not afford to live inside the zone but need to drive there for their work do end up paying. It would make more sense to tax the actual use of the roads inside the area instead of the mere fact that a vehicle crossed some imaginary border between the untaxed and taxed zones.