This.
It can be a pain to get to cheaply though.
We went over land via Bulgaria and Serbia. Which in itself was AMAZING. Serbia is utterly beautiful (Belgrade is a bit of a dump but very interesting none the less)
I'd also recommend independent travel around eastern Europe generally.
We've also done Dubrovnik into Bosnia going to Mostar and that's fabulous and a little easier (you can then go on to Sarajevo that way).
Pula (Croatia) and then travelling down the islands along the coast and going inland to Plitvice National Park is wonderful.
Tallinn is a fab little city break. Riga is small but pretty - we hired a car and went down into Lithuania to a gorgeous castle.
Fly into Malaga, hire car and head north into the hills - if you leave the coast it's brilliant. we headed up to Seville via a bunch of beautiful unplanned stop offs .
Also fly into Barcelona and go up to Zaragoza and Montserrat.
Finland. We loved Helsinki. We went in winter and went out to islands through the frozen sea but travelling north doing a Finnish castle (fab) and seeing a friend in Tampere (also a pretty little town).
I have down Copenhagen and Stockholm again great cities but I'd love to fly into Copenhagen and get the train over to Malmö and explore around that area.
The Netherlands is just great for independent travel. Its easy and I'm very fond of it. Rotterdam, Eindhoven, Utrecht and The Hague and all good cities and if travelling by car there are plenty of places in between worth stopping off at. You can head south into Belgium - Antwerp is pretty.
Tenerife. Yes really. But don't go to the more touristy places. Hire a car and go to the north of the island.
We did a Wroclaw city break and I enjoyed that.
We like to fly to cheap places and then explore if we can. It takes planning - wikitravel is a really easy and cheap place to start to get ideas for places outside the city or you think about getting the train / driving to another nearby town or city.