The colony town was filmed in Pickering, Ontario, which is also the filming location for the series Reacher (2022), the film It (2017) and many other series and movies.
The class of the USS Cayuga has not been specifically identified on screen, Memory Alpha notes that it could be either Constitution-class or Sombra-class as they look nearly identical, the USS Peregrine (NCC-1549) in All Those Who Wander (2022) was Sombra-class. This episode reveals the registry number of the Cayuga: NCC-1557, from that it can be inferred that the Cayuga is almost certainly Sombra-class. This is because the USS Constitution, the prototype and first ship of the Constitution-class, has a registry number of NCC-1700; the Enterprise was the second Constitution-class starship with the registry number NCC-1701. The Cayuga's registry number being lower than the Constitution indicates she was built earlier, by a bit in fact.