I've been a lot of places (somewhere near 40 countries) but strangely I couldn't really come up with even 5 cities. I tend not to spend a lot of time in cities. When I go somewhere for tourism it's usually in nature (so I'd recommend Rangiroa in Tahiti but there are only about 100 people there so that's not a city, or Whistler BC, which is a town). Punta Cana was nice but I never left the resort so that doesn't count.
As far as cities go, Budapest is #1 on my list, but I lived in Hungary for 2 years so I got to know it well. Prague was the nicest city I've ever seen in a quick-hit tourist sense, just gorgeous architecture. Tashkent is the place where I had the most unique experience but I can't go into detail. Valletta wasn't that nice (but not bad) but it felt like the set of a James Bond movie so it had a level of exotic to it. Edinburgh wasn't my bag because I'm not so much into British culture but it's scenic and I spent the millennium New Years there so had quite a party. Venice is dirty but also romantic (too bad I was there with a dude) but worth at least an overnight visit because it's so unique.
The best places are off the beaten path; I was heading to Vienna from southern Hungary once but we got a late start and ended up going through some small Hungarian town with a weird large hill in it. There was a castle at the top of the hill. We decided, fck it, lets skip Vienna and just go up to see the castle. They had a crazy medieval show up there and it cost about 50 cents, we had a nice day and then just went back home, a unique experience I'll never forget.
In the US I'd say Seattle (but grew up there so I'm biased), Park City (lived there too), Bend in the early 90s, Kailua HI (lived there too), Sandpoint, ID (family from there but it really is beautiful). I don't have much east coast experience but I lived in DC three different times and it is really pretty beautiful there if you can avoid the traffic.