Moscow,
Paris,
Rome,
Copenhagen,
Talinn to name 5 but so many are wonderful. You can add Prague, Budapest, Krakow, St Petersburg, Stockholm, Venice, Barcelona, Dublin, Munich, Salzburg and vienna to the list to name but a few more that are well worth the visit.
Paris (with partner - no so good with the 'lads') Brussels (no, really the beer is FANTASTIC) Amsterdam (say no more) Turin (visit all the locations in The Italian Job) Porto (port, fish and a lovely sunset location)
These are five of the places I have visited, and all are excellent, albeit mainly noted for food and drink (except Turin).
Big shout for Reims (pronounced 'Rance') and Epernay. The places themselves are unspectacular, but they are great for sampling Champagne at source. You get it about 40% of the price we pay for it, and it is the closest French wine-growing region to the UK.
Don't bother with Eastern Europe, not much to see, grumpy locals and well geared up to rip off the English.Esp Budapest, absolutely no cheaper than London.