Well, it does vary from city to city and from home to home.
Our property taxes are around $1200/yr. We have friends with similar sized homes with much higher values in other parts of the city and in suburban cities who pay 2 to 3 times that.
We've not made any decisions on schools yet, but just looked at the tuition at Saint Mary's in German Village, which was around $5,200/year. The "EdChoice Scholarship Program" that can be applied for to send kids from poorly performing schools to better schools is currently $4,250/year, making Saint Mary's around $1000/year.
So if our taxes stay at $1,200/yr (and I'm sure they won't) and we're paying $1000/year for private school (which is our backup option at this point), that $2,200/yr cost is still less than what we'd be paying for a similar home located in Dublin, Bexley, Upper Arlington or elsewhere that we've known a lot of friends to move for the good public schools.
But again, it does vary from city to city and from home to home and situation to situation.
There are some good options and alternatives out there though for urban inner-city neighborhoods.