Weekends

In Rome and Venice (just to complete the answers) yes.

I can't say for Rome and Venice, but in London and Paris yes.

If you run into closed site it will be mostly likely on Monday. For the most part we plan for Monday to be an off day.

My experience in Italy has been similar to Frank's. Things tend to be closed Monday. You might find some churches that are closed to tourists Sunday, or at least Sunday morning, since they are doing services at that time.

In my experience, weekends are big tourist times, and on the free days (usually particular Sundays)lots of locals visit their museums and sites also. Keep in mind that any churches you want to visit will be having services on Sundays and at other times, and will be restricted for sightseeing.

The only thing you might run into is shops being closed on Sundays, and it's not uncommon for them to close early (around 5, maybe earlier) on Saturdays.

In London, the local folks who work M-F also sightsee on the weekends so things are that much busier.

Also London Underground tends to shut down vast swathes of the Underground (tube) most weekends for construction / maintenance. You see more at bus height, but it is slower.

You've never lived until you have heard the bells of St Pauls Cathedral ringing before the Sunday morning service. If you stand near the Paul restaurant on the north west corner you will feel that the sound just washes over you like waves.