I love visiting The City during the week and on the weekend.
During the week the place is a fabulous bee hive with all the hustle and bustle, my favourite burrito place is open, it is easier to get into many of the churches during the week when they are open and have a look around, the buses are at their most frequent, and everything is open.
During the week it can be a madhouse, especially near and during both rush hours, and the lunch "hour" (Emma says blythely "hour", but she doesn't appear to work in The City, where many people run out and grab a take away and eat it at their desks - more like a lunch 10 minutes) can really seem like a third rush hour. Don't get in the way of those people.
For me I also love The City on weekends, especially Sundays, because I can park my car very easily, there are few to no parking restrictions on a Sunday (even after one on a Saturday), I love church bell change ringing, and I walk the lanes, courts, and little roads in peace, exploring all the architecture (laughing or gagging at most of the modern stuff) and reading blue plaques to my heart's content. There's even a blue plaque (and other memorials) app now - very good.
For the bells on Sunday, on most Sundays, there is the lovely melodious noise starting at St Pauls and continuing at St Vedast Alias Foster, St Mary-le-Bow, St Lawrence Jewry, St Clement Danes, and back to St Pauls. I love it.