At first I thought the poles (of the planet) might be good. The cooling is basically free. But the energy and internet connectivity would be a problem. At the poles you can really only get solar about three months a year, and even then you need a lot of panels. Most of Antarctica is powered diesel because of this.
So the next thought was space. At the time, launching to space was way too costly for it to ever make sense. But now, with much cheaper launches, space is accessible.
Power seems easily solved. You can get lots of free energy from the sun with some modest panels. But to do that requires an odd orbit where you wouldn't be over the same spot on earth, which could make internet access difficult. Or you can go geostationary over a powerful ground station, but then you'd need some really big batteries for all the time you aren't in the sun.
But cooling is a huge problem. Space is cold, but there is no medium to transfer the heat away from the hot objects. I think this will be the biggest sticking point, unless they came up with an innovative solution.
Geostationary satellites only go into Earth's shadow on around 20 days on each side of an equinox. That leave 280+ days each year where they are in sun all day. Maybe that's enough to be worth it?
Or if you do need to keep the things working even on those ~80 days a year when they do spend part of the day in shadow maybe they could be powered by energy beamed in from those not in shadow? You'd put a bunch in geostationary orbits spread out evenly so that each is close enough to its neighbors for power beaming.
I wonder if something crazy might work? Could you actually connect adjacent satellites by an actual physical power cable, which would also be in geostationary orbit?
I'd guess you'd actually need two conductors in your cable, carrying current in opposite direction to cancel out interactions with Earth's magnetic field so the system doesn't get pushed out of its orbit (which would probably be bad).
There would probably be gravitational interactions like with the Moon that might also make it hard to keep everything in place, but maybe by purposefully sending different currents in opposite directions on some of the links you could purposefully use interactions with the Earth's magnetic field to move the cable back where you wanted?
If the satellites are connected by cables then maybe they could actually be slightly higher than geostationary but moving faster than circular orbital speed at that altitude so there is a net outward force from that, which could be countered by tension in the power cables to force them into a circular path that is still geostationary.