Finding a city in which household gun ownership rate is high and the crime rate is atypically low should not be difficult -- any city in Wyoming will do. Can you find a city with similarly low crime rate and similar demographics where the rate of household gun ownership is significantly lower? If so, you will next need to consider gun control laws in the two cities. Doing this so your findings are valid -- you've controlled for all known relevant factors -- will not be easy. Correlation is a necessary but insufficient condition to prove cause and effect.
Can you find a city with a high rate of household gun ownership and a correspondingly high rate of crime? I suspect you can. You might try New Orleans, for example. I strongly suspect you are on a fools errand here. Why do I think that? It's because my unreliable intuition tells me that most crooks have not studied household gun ownership statistics, and they don't know ahead of time whether a home owner has a gun or not. My intuition tells me that a crook is far more likely to have taken account of whether someone is home than he/she is of household gun ownership statistics. And probably equally likely to have made note of whether there appears to be a surveillance/alarm system. My intuition tells me that affluent home owners are more likely to have operative surveillance/alarm systems than less affluent home owners. I trust your observations have taken that factor into account. But remember, my intuition is as unreliable as yours.
Careful studies of gun crime statistics and statistics bearing on the effectiveness of gun control measures do exist. They are surprisingly numerous in fact, especially considering how often their findings are misquoted or ignored by the gun lobby, politicians, the public and the media. I suspect that ignorance of these many studies is nowhere greater than right here in these ET forums!
https://www.hsph.harvard.edu/hicrc/firearms-research/gun-threats-and-self-defense-gun-use-2/
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