Does having bigger wheels mean less effort pedaling? Assuming that we are using a fixed-gear bicycle and width of the wheels are the same, I wondered, does having bigger wheels mean I need to less effort to get from point A to point B in an urban setting? I'm thinking based on the formula for circumference: 



Where r is the radius of a bike wheel. Additionally when looking at this gif for a vertical visualization of circumference:



It appears that having bigger wheels will get you from point A to point B in an urban setting with less rotations by the wheel, but does that also mean I need to work less to get there? What about uphill? Does having bigger wheels help/hurt biking uphill?
Assuming a completely smooth road and neglecting the weight of the wheels, it makes no difference: you still need to do the same amount of work. Essentially, larger wheels give you a higher gear ratio, so doubling the diameter of the wheels would mean you'd only need to turn them half as many times, so you'd only need to turn the pedals half as many times, but you need to press twice as hard on them.

But, in reality, there are limits to what you can do. If you need to lift 100kg of wood, it's easier to lift 10kg at a time, even though the total work done is the same as when you lift the whole lot at once. Similarly, you'll be more physiologically efficent (and comfortable!) pedalling with certain ranges of cadence and force.

Bigger wheels roll over bumps better. As an easy thought experiment, consider a pit whose width is equal to the diameter of your wheel. Obviously, the wheel will fall right into the pit. But if you consider a wheel with twice that diameter, it will only drop a little way into the pit as it bridges over it.

In practice, though, there aren't a whole lot of wheel sizes to choose from.  Either you get a folding bike with small wheels, or you get a non-folding bike with wheels about 62cm/29in in diameter (or about 56cm/26in for mountain bikes).