Places worth one week?
I work it a little backwards. First go to Tripadvisor and look at a list of attractions. Decide what attractions are must see for you. Plan two big sights a day (one AM, one PM). Between breakfast, sight, lunch, sight, and dinner, you may have room for some minor sights. I keep a list of "good to see if I have time" sights for late afternoons/evenings when I still have energy. They also come in handy when your preferred sight is either closed or didn't take a half day to see. Keep in mind, some sights take more than a half day to see. Test each place you think might be a good option and see if it's worth a week for you. What's worth a week to me may not be for you, and vice versa.
That said, for me Rome, London, and Paris certainly have plenty of sights to keep almost anyone entertained for a week. So far, I've spent a week in London and Rome and felt like both needed significantly more than just one week. I've spent at least three weeks total in Paris (during eight visits) and still haven't seen everything I'm interested in.
Barcelona makes it if I add day trip sights from there. Without daytrips, I would want three full touring days to see the sights that interest me.
I have yet to visit Vienna. It seems to be a place where a week wouldn't be wasted. Salzburg is lovely but it wouldn't rate a week for me.
I have also not visited Lisbon.
Of the Scandinavian cities. I could spend a week in and around Copenhagen (Copenhagen Card includes area train travel and admissions).
Spanish cities of Seville and Grenada don't quite need a week for me. Both have a pretty good list of sights.
I love northern Italian cities like Venice, Siena and Florence (in fall). Florence comes the closest to having plenty of sights for a week.