New Berlin is a city on Earth's moon and probably part of the Lunar colonies. It was founded sometime prior to 2067, as Jonathan Archer mentions it existed prior to the launch of the SS Conestoga. (ENT: "Terra Nova")
Sometime prior to 2143, Archer's then girl-friend Caroline moved to New Berlin so he decided to get drunk in 602 Club.
In 2143, New Berlin detected the NX-Beta, an early warp ship, leaving Earth's orbit for an unauthorized flight piloted by Jonathan Archer and A.G. Robinson, so then-Commodore Maxwell Forrest could witness the ship achieving warp 2.5. (ENT: "First Flight")
By 2373, New Berlin was large enough to be seen from Earth at daytime, since Commander William Riker missed the familiar sight of the city, while looking at the Moon during his mission to the year 2063. (Star Trek: First Contact)