How to save money on a long term car rental in the US?

I'd like to travel in the US for 3 months (I'm a foreigner). I know it's a lot easier getting around if I have a car than public transportation in the US. What's the cheapest way I can have car transportation while I'm in the US?

I'm leaning towards traveling from Florida to New York. But I might go from California to Nevada, Arizona, Utah, Wyoming, Montana, South Dakota instead. All one way travel. Thanks
 
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