I'll be traveling around Europe for about a month. Have already visited Munich, Prague, Paris, Strasbourg, Florence, Naples/ Amalfi/ Sorrento/ Capri, Lyon, Geneva, Copenhagen, Dublin, and London and want to visit new places. Am thinking Norway, Sweden, St. Petersburg, Poland, Berlin, Slovakia, Budapest, Vienna, Barcelona and...? I'm not committed to any of those and am open to any suggestions on your favorite places in Europe - either in those areas or outside, small towns or big, well-known or hidden - anywhere in Western or Eastern Europe or Scandinavia. Very flexible! Also would love suggestions on good friendly hostels (safe!) as I'm a female traveling solo. Thanks much!

From your list, Berlin is my favourite city in Europe, and Slovakia one of the best countries to travel to imho.
Berlin is an extremely fascinating city. I've been there 5 times now and I always come up with unique places in Berlin I haven't been to yet, and others I want to revisit of course. If you're into history, it's everywhere. Also, it has the most green areas of any European city (my own favourite parks being Görlitzer Park, Treptower Park, and the garden of Schloss Charlottenburg). And there's good nightlife no matter what kind of music you're into. On my first visit a couple of years ago, I stayed at the Backpacker hostel on Chausseestrasse in Mitte, which I would recommend, and I've also heard good things about the Circus and Odysee hostels in the same area.

Slovakia's especially great if you want beautiful nature, small towns (and even Bratislava is relatively small and quiet compared to Prague, Vienna and Budapest), hiking, ruined castles, friendly people, etc. Also it's dirt cheap, at least for western tourists. In Bratislava, the Bernolak is a good place to stay (only open during the summer holidays though; you get your own room with private bathroom, and the bar downstairs is good for meeting others). In Kosice, the hostel (don't know that name but I assume it's the only one there) isn't particularry good as a meeting-place (no bar, kitchen or common room, and very few people staying there anyway) and it has a midnight curfew (they're not too strict about this though), but it is cheap, and you get your own room and a shared bathroom with just one other room. Those are the only hostels I've stayed at, in other places I stayed at hotels, private rooms or camped.

Another recommendation I would add is Serbia. I've spend 3 weeks there in 2001, and it was one of the best trips in my life. There's hardly any western tourists that go there, so people smother you with kindness if you do go. (if you want any more info on places to go there, let me know)

You can try Poland and Sweden.

Poland is a great country to visit. Lots of history and quite a few cool places to see and things to do. Cities you should visit:

Gdansk - On the coast of the Baltic Sea. Incredible Old Town to explore. When in Gdansk you can also visit Sopot, relaxing beach town a short hop away. Stay one night at the Grand Hotel Sopot, right on the beach. In its hayday Polish movie stars and sigers used to go there for R'n'R. Now they go to Jurata, on the Hel peninsula.

Krakow - City full of history, the most well know travel destination in Poland. It will take you a few days to explore everything Krakow has to offer. A must when visiting Poland.

Warsaw - Capital city and backbone of Poland. Visit to see the tall buildings and enjoy the best restaurants in Poland. Can be a bit pricy, so stay just enough to enjoy the place.

Wroclaw - In Souther Poland, about 2 hours away from the Czech border. Great old town and scenic spots around.

Jelenia Gora - Almost on the border with the Czech Republic. Stay in Karpacz, 30 minutes or so from Jelenia Gora. Great hiking.

Zakopane - About 3 hours from Krakow. Another mountain get-away.

And many other places to visit and explore.

Sweden - Great scenery, cool people and Stockholm is one of the most incredible cities in Europe...just bloody expensive. You can head on north to experience the wilderness of Sweden. Great hinking and skiing.

You can hop on a boat from Poland to Sweden. It takes about 17 hours from Gdynia to get there. Happy travels!

Hi

Barcelona is one of my favourite cities and worth a visit at any time of year. The Mercury fountain in the Fundacio Miro is worth 30 minutes of anyone's time.

I've stayed both upmarket and hostel in the city. The Gat Raval last year was a rather friendly place but is on the edge of a rather seedy area with prostitution and some drug usage. A very short walk to 'safer' areas though and there were always plenty of people about, so it wasn't particularly intimidating.

Unfortunately hostel prices in Barca are often quite high and small hotels might offer better value and locations. Food and drink are fairly cheap for a major western European city, though, so that is soe compensation.

A female traveling solo will feel safe and relaxed on the Lofoten islands, despite the wild and dramatic shape of the nature there. The two Lofoten websites:
http://www.europe-holiday.com/user/lofoten/en.htm
http://www.europe-holiday.com/user/nordland/en.htm
will show you some of the islands aweful beauty.
Here you may also experience the Viking time: http://www.lofotr.no