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***SPOILER ALERT***

During an interview following the Batwoman finale, the location was revealed (at least one of the locations- some more may be determined later):

During an interview with the International Business Times following Batwoman’s season finale (which featured a major DC reveal), showrunner Caroline Dries revealed the Superman/Batwoman crossover will take place in Smallville, which is where Superman & Lois will be set. “I have a little bit of research, but they don’t have any scripts out yet, like that’s been released, so nothing’s been shot,” Dries explained. “So obviously I know about ‘Superman & Lois’ and I know it will be taking place in Smallville and all the rest is to be determined, but it’s going to be a great challenge because those crossovers always end up so awesome.”

Source: ScreenRant

“Superman and Batwoman will be coming together in a crossover event for The CW.

The CW Chairman and CEO Mark Pedowitz revealed on the network’s scheduling call that it would be planning a two-hour event pairing the two superheroes.

He said it would not happen in December, given the COVID-19 production shutdown, but hoped that it would happen in either the first or second quarter of 2021.

‘We’re still working on it. It will be a smaller event than usual, we’re only planning a two-hour event. We are talking about doing Superman and Batwoman together. There’s a lot of characters coming from our other shows,’ he said.”

Source: Deadline