Hypothetical questions are always really fun in science because they make us think about what we know in a different light, which can make us better understand the huge scale of our planet. So let's stop the Earth from spinning and see what happens.
First of all, let’s imagine the rotation stops in one second. At the equator, it's like being in a car that was moving at 1,670 kilometers (1,038 miles) per hour and hitting the breaks. If you are in a building you’ll be thrown into the closest eastward wall and experience 47 times the gravitational acceleration of our planet. The good news is that this might not kill you. But everything else will.
The Earth might be still but everything else will continue to move at exactly the same speed the Earth was spinning before. This includes the atmosphere and all of the oceans. The winds alone would be four times faster and stronger than the fastest wind ever recorded (408 km/h 253 mph). And then you’ll experience a huge tsunami wave, which will destroy anything the winds didn’t (which may not be much).
The extent of the damage will obviously be more devastating the closer you are to the equator but in the long run, being near the poles won't save you either. Due to its rotation, the Earth bulges in the middle, so the poles are about 21 kilometers (13 miles) closer to the center of the Earth than the equator. Without the rotation, the oceans will migrate towards the poles – where the gravity is strongest – creating, respectively, devastating Earthquakes, one very large megacontinent across the equator, and two separate oceans.
According to Witold Fraczek from the mapping and analytic company Esri, the north ocean will host most of Europe and Russia underwater. Greenland and all of Canada will be submerged as well as Chicago, Seattle, and Boston. New York will still be near the ocean, just in a different direction. In the Southern Hemisphere, the ocean will have covered huge chunks of Argentina, Chile, and New Zealand, as well as the whole Antarctic continent.
So if your supervillain plan is to slow down the rotation of the Earth, the best place to be is at the North Pole on a well-equipped floating mobile base. The location would certainly be an advantage. The Earth would experience a "day" every year, so by going around it would be possible to simulate regular day/night cycle. But things won't be too rosy in the long run. A non-rotating Earth will not have a magnetic field, as the liquid core of our planet would also be stationary. Without the magnetic field, the few living creatures that could have survived such cataclysmic changes would eventually succumb to the radiation.
If you had more time you wouldn’t have to worry about actually slowing down the planet, the Earth is already slowing down on its own. In the last century, the length of the average day has increased of 1.7 milliseconds. The long-term trend is due to tidal effects between the Earth and the Moon but the length of the day also fluctuates due to other effects. At this rate, it would take 18.5 billion years for the Earth to have a day as long as a year.