The single most common European-trip mistake is the wrong day-count per city. Three days in Rome is not enough. Six days in Bruges is too many. Two days in London is a waste. The right number per city depends on what's there to see and how much the city rewards slow time.
This is a per-city honest answer for the 30 cities most travelers consider.
Cities that need 6+ days
Rome. The Vatican alone is a half-day. The Forum + Colosseum is a half-day. Trastevere evenings need their own night. Roman day-trips (Tivoli, Frascati) deserve a day. 7 days is generous; 5 is the floor.
London. The free major museums alone (British, V&A, Natural History, Tate Modern, Tate Britain, National Gallery) are six half-days. Plus West End theatre. Plus day-trips to Bath/Windsor/Cambridge. 5 days minimum.
Istanbul. Big enough that even one section (the historical peninsula) is 2 full days. Add Beyoğlu, the Bosphorus, an Asian-side ferry day, and you're at 5-7. 6 days is right.
Berlin. Wide-spread, with Museum Island, the Wall memorials, multiple worth-it neighborhoods. 5-6 days for first-time, 7+ if your trip is dinner-and-nightlife focused.
4-5 day cities
Paris. 4 days is enough for first-timers focused on the major sights and a couple of neighborhoods. 5 if you add Versailles. Less than 4 leaves you exhausted.
Madrid. 3 full days is the museum minimum (Prado, Reina Sofía, Thyssen). 4 with a tapas-walking weekend.
Barcelona. 3-4 days for sights + beach. 5 if you add Montserrat or a wine-tour day.
Florence. 3 days for the Uffizi-Pitti-cathedral circuit. 4 if you add Fiesole or a wine tour. Florence empties faster than expected.
Vienna. 4 days for the imperial-Vienna circuit + the cafés. 5 if you add Schönbrunn at leisure or a day-trip to Bratislava.
Amsterdam. 3-4 days. The city is small but the canal-walking + museums + bike-around fills the time.
Athens. 3 days for the central archaeology + Plaka + at least one neighborhood like Koukaki. 4 if you add Cape Sounion.
3-day cities
Lisbon. 3 days covers the major hilltops (Alfama, Príncipe Real, Bairro Alto). Add Sintra as day-trip 4.
Porto. 2-3 days. Smaller and more concentrated than Lisbon.
Prague. 3 days. After that the central old-town wears thin.
Budapest. 3-4 days. The two sides of the river plus the thermal baths plus dinner culture.
Krakow. 3 days. Plus a day for Auschwitz.
Copenhagen. 3 days, 4 if you add Helsingør or Roskilde.
Stockholm. 3-4 days. The island-hopping is part of it.
Dublin. 3 days. After that you're really doing Ireland not Dublin.
2-day cities
Bruges. One full day + an evening + breakfast. Anything more is repeat-walking.
Sibiu. Two days max for the city itself.
Mostar. One night at most. The city is one square + the bridge. Better as a Sarajevo-Dubrovnik stopover.
Cesky Krumlov. One night.
Salzburg. 2 days for the city + Festung + Mirabell. 3 only during the festival.
Galway. 2-3 days, primarily as a base for the Cliffs of Moher.
Reykjavík. 2 days for the city itself; everything else is the rest of Iceland.
1-night cities
Pisa. The leaning tower is 90 minutes and you've seen the highlights. Don't sleep there if you can avoid it.
Bratislava. 1-2 nights as a Vienna add-on.
San Marino. A long day-trip.
Most ski-villages. If you're not skiing, one night.
The rule
If a city has fewer than 3 worth-it days, you're better off as a day-tripper from a real city. If a city has more than 4 worth-it days, you're robbing yourself by trying to "fit it into a one-week loop."
The classic mistake is the 14-day, 7-city European loop. Almost no European trip benefits from changing hotels every other night. Pick 3-4 cities for a 14-day trip, with 3-5 nights each. The rest is wasted on transit.