> You'd have to build a fully underground cooling system that goes to a nearby river (or huge lake) and use the cold water from that, which would get costly quick.

Helsinki gets its water from the 120 km Päijänne Water Tunnel, which cost €200-250 million (adjusted for inflation) to build. Peak flow is 10 m^3/s by gravity alone and up to 20 m^3/s with pumps, which should be enough to cool a 1 GW data center. You could increase the cost by 2x (because real wages have gone up), by another 2x (because middlemen have destroyed productivity), and by yet another 2x (because everything is more expensive in America), and it would still be pretty reasonable.