The answer will vary based on latitude since the earth's rotational velocity is a function a distance from the axis of rotation, e.g., 1000 mph / 1600 kph at the equator, 0 at the poles. Since the equator is the worst case, I will use that. Since mach number is temperature dependent, mach 1.3 is just an approximate reference value for your flying city.
Also, not clear from your question whether you will be the only population on earth, so I will assume you are not as this adds some issues to consider.
Elevation? High altitude means lower air pressure (reduced drag, etc.) but means you have to pressurize your city. If you needed to supply a pressure of 1/2 atmosphere, you have a static load over 1000 lbs / sq ft or about 5000 kg / sq meter. Not very high pressure for a tank, but building a pressure vessel the size of a city will have challenges. Extra complications if you want to live in a clear dome. But overall, higher is probably better in most respects. Radiation is not once of those. High elevations means you will encounter a lot more radiation. Anything over 10,000 meters is too high over a long term unless you add radiation shielding.
Air turbulence. You will have to completely seal your city from the environment. At Mach 1.3, everything your city would be ripped to shreds by air turbulence (ripping up trees, buildings, etc.) if not encased. You need a strong container to resist not only air forces, but also deal with things like running into a flock a geese. They are low grade canonballs under your conditions.
Drag? Does your unobtanium magically hold in in place relative to the sun, or you do have to supply the power needed to propel the city against the wind. Since you are flying a city at greater than mach 1, you will need power and lots of it (billions of watts, maybe trillions) to counteract drag. Since you exceed mach 1, there is not much you can really do about it, i.e., streamling only gets you so far because you are compressing the atmosphere to punch through it at high speed.
Cooling your city. Remember that due to air compression, you are going to encounter high temperatures from the compressed air. You also have to get rid of the heat from generating all the power to counteract drag. So you need to run the biggest air conditioner in the world 24x7. You cannot use the ambient air to cool your city since it will heat up by around 100 C when you attempt to use it this way.
Noisy neighbor, you will be the noisiest neighbor in existence. The sonic boom that you generate will be huge, and you will overfly each point on your flight path once per day. Nobody is going to like you.
Economic logistics. Unless their is also a different kind of unobtanium, everything you do will cost more as the difficulty of moving everything to and from your city will be quite difficult. In fact, no jet on the planet could safely land on your city today unless you build an entirely unique airfield that brings air to rest relative to your city and still be an open air field. Perhaps if your city is large enough, your could design a leeward hanger deck that is open air large enough support the necessary air traffic. Remember that your service craft will also have to have mach flight -- unlike any existing cargo planes.
Equipment maintenance. You will have to power your city's flight with the equivalent of fighter jet engines and a lot of them. Maintenace on such systems is very high, lots of downtime, inspection, replacement parts., etc. So you have to have lots of extra capacity, the ability to redo the parts from scratch (i.e., smelting, etc.) and trained personal pulling maintenance.
Self-sufficiency If you are the total population you will of course have to be self sufficient. A lot like a colony on mars, except you have a few advantages, mostly freely available air and water (i.e. collect the rain, assuming you are not too high or condense it out of the air). However you will presumably need to replenish supplies for energy, etc. so the logistics statements already mentioned still apply though they would be less frequently needed
Construction. Building all of this while under attack from your night creatures won't be a picnic either. Under the most optimistic assumptions, this city would be incredibly complicated, expensive and time consuming to construct initially. Much worse than going to the moon.
24 hour sunlight would be way down on the list of your problems. Hang some curtains.