In high school I had a boyfriend who was obsessed with low gas prices. We lived 30 miles away from each other (I moved halfway through hs) and gas was generally cheaper in his county. When I knew I was headed that way I'd wait to fill up, saving 10-15 cents a gallon*. If he got in the car and saw that the gas was low he'd want to drive 3 towns over to fill up. The savings was usually 2-3 cents a gallon and back then I though it was crazy to drive 10 miles to save what amounted to 20 cents to fill my 10 gallon tank, so I tried to fill up before I saw him.
Though gas prices are crazy (!) I still feel the same way. If I know I'll be in a part of town** with cheaper gas I'll wait. Otherwise I go with the best of my available options. For me the best way to break it down is by the difference in price. Lets say gas is 4 cents/gallon cheaper 3 miles away. Filling my tank usually takes 10 gallons. That means I will save 40 cents on my bill.
Currently I get around 30 mpg when I drive. This handy tool tells me paying $3.60/gallon equals 12 cents per mile***. So driving 6 miles, round trip, out of my way will cost me 72 cents in miles. My 40 cent savings for the lower gas price is eaten up and the transaction ends up costing more financially. It also takes up your time.
The number will vary based on your car's mileage and the costs in your area, but the moral of the story is chasing the best price won't always save you money. Even if your tank takes 20 gallons saving 5 cents a gallon means saving $1.
*Back in the days of $1.50-2.oo gas.
**The upside of driving all over the city is this is relatively easy to do.
***A 4 cent fluctuation doesn't change the price per mile.