Does it really make sense to drive your vehicle to another gas station from 3.75 to 3.78

Let's do the math. Most cars have around a 10-12 gallon tank. So if you are completely empty and fill up you would save 30¢ to 35¢. Now to me, that's not exactly worth driving a long way for. Even if you had an SUV with a 20 Gallon tank, you would only be saving 60¢ Again, not worth a lot of driving if you ask me.

suppose you put in ten gallons of gas, you would save thirty cents. If you got twenty miles to the gallon and drove one mile to another gas station you would use up 20 cents. if you start and stop during that trip you would use up more and if you turned the engine off and then started back up you would use much more gas. So unless you driving past the $3.78 station to one a block away it's not worth it or even more expensive.
And if you have a longer wait to get gas your time is probably worth more the thirty cents.

If it's far away then no b/c you'll waste money in consuming gas just to get there and save 3 cents a gallon.

Only if the station is right next door.