I live in the City of Atlanta (not the suburbs), biking distance from downtown or midtown, in a 3bed/2bath 1500 ft2 house. Assessed value is $115K, but actual value is probably closer to $150-200K. If I renovated the kitchen and bathrooms, it would be worth $300K+.
My taxes are $1200 this year (up from $650 in 2013, when the assessed value was really low). My next-door neighbor's taxes are $3500/year on a similar-but-renovated house, assessed at $285K.
There are two interesting things about how property tax works around here. First, we have a Homestead Option Sales Tax (HOST) which subsidizes the first $X worth of property value from sales taxes. For a cheap property like mine, it probably cuts my tax nearly in half compared with it should be based on the millage rate. (Conversely, it means the tax penalty for making improvements is larger than what it would otherwise be, which is unfortunate.) Second, capital improvements to the school system tend to be funded by a Special Purpose Local Option Sales Tax (SPLOST) instead of property tax. Between the HOST, SPLOST, MARTA (transit) sales tax, and the additional MARTA and transportation sales tax that I hope we pass later this year, our sales tax will be up to 9%, I think.