Ironically it was the total destruction of the Old Town that allowed these walls to be rebuilt after WWII and today the space in-between the two historical brick ramparts forms a pedestrian promenade parallel to ul. Podwale known as 'Międzymurzę.' Along this pleasant route you'll find many historical plaques and monuments - including the Kiliński and Little Insurgent monuments, but you won't see much of the Old Town centre, as the view is obscured by the high inner wall. During the holiday season, this promenade is the site of one of Warsaw's best Christmas markets.
You can learn more about Warsaw's Old Town defensive walls by visiting the seasonal outdoor exhibit in the Barbican from June to mid-October (open 11:00-18:00, closed Mon; admission 6/4zł).