The part of a Halo 2 level that was shown at E3 in 2003 morphed into what eventually became two levels, Outskirts and Metropolis, roughly divided into Old and New Mombassa, respectively, the city being divided into two parts by a river and connected by a bridge.
The Sword Flying trick was first extensively demonstrated on Metropolis. The procedure for executing it is somewhat complicated; it involves parking a Warthog in an area where a Phantom attacks, targeting the plasma sword on one of the Phantom's turrets, and then waiting until the Phantom has withdrawn before exiting the vehicle. You will be propelled in whatever direction you face; this method can be used to extensively explore the level, including otherwise unreachable areas and is a way to retrieve the Scarab Gun without a Banshee (although you can't get back down with it...)
The Cairo Station level is where you really start to feel nostalgic, not only for Halo 1 but for much older Bungie games. The parallels to the first Halo game start to become apparent, as well as the influence of ideas and themes from the Marathon series.