First off, I'd recommend flying Iceland Air. It's cheaper than a lot of other airlines, plus they allow for stopovers (at no extra charge) in Iceland. I only spent a few hours there, outside Reykjavik at the Blue Lagoon, but it is absolutely fantastic and I plan on going back - definitely take advantage of it.
Personally, I was very underwhelmed by Prague. It had it's beauty and it's interesting bits, but I spent 3 days there, and it was 1 too many. Maybe it's because I went in February, but it was not my favourite trip. Best part of the trip was seeing Carmen at the opera.
I LOVED Berlin. Not as aesthetically beautiful as some of the more 'classic' European cities, but there's so much to do. I love exploring places with history and culture, and in Berlin it was a couple of days of WWII things, then on to the Cold War, then on to the Berlin Wall - so much!!
Rome is fantastic. I loved the tour I did of the Colloseum and Roman Forum, as well as touring the Amalfi Coast and Pompeii. And the food!!! If you love pasta, of course it's fantastic. I'm an odd person who hates pasta, but even I was stuffed all the time, if only from the bread, cheese and proscuitto!
I enjoyed the French Riviera, but if you go there, it's advantageous to know that the beaches are not what you'd expect. In Nice they are large stones - very uncomfortable to walk on, and making it challenging to get into and out of the water. In Monaco it was smaller pebbles, so more manageable. In Cannes there's actually sand (apparently it's shipped in because of the film festival). Nice is a great base to do day trips. The 'old town' area is where I stayed and I remember a lot of smaller almost alleyways filled with restaurants and very charming.
Stockholm is an absolutely gorgeous city. It's also an extremely walkable city, and almost everyone speaks excellent English, which makes things a lot easier. The city is split into different islands - the Old Town is the most historical area, complete with the royal palace, but from there you can see Djurgarden, where there is everything from an ABBA Museum to the Vasa Museum, which houses an amazingly restored boat that sunk on it's maiden voyage in the 1620s.
One thing I started doing when I travelled in Europe is seeing if
Sandeman had a base in the cities. Sandeman will offer a free tour of the cities but also various paid tours. I would do the free walking tour on my day of arrival or the next day (depending on my arrival time) - familiarized me with the city and kind of let me know what I wanted to learn more about, or any other tours I'd want to take. Then I would often take another of their paid tours once I knew what I wanted to see - you can buy the tour passes on the free tour, and they usually start just after the free one ends. It's a great way to get to know the city you visit. This is also great if you're a solo traveller, like I often was.