Vidya, that's an easy one, all other things being equal stay in Budapest. It's easily a three to five day visit if you do just a minimum of planning. Where in "Eastern" Europe are you going? When in the Summer? Maybe I can help you find some special things to do during your stay.
Here is a hint. When I market Budapest I love to call it Eastern Europe because that is what it is to most Americans and it brings to mind exotic or radical or mysterious. Most all of what American's call Eastern Europe the Europeans call Central Europe. That includes, Poland, the Czech Republic, Romania, Hungary, Croatia, Slovenia, Slovakia and the countries of the Balkans. What is left for Eastern Europe? Ukraine, Moldova, Belarus, Russia (part of), Georgia, Armenia (the line between Europe and Asia gets a little foggy at some point). If you read Churchill's famous "Iron Curtain" speech where he coins the term "Iron Curtain" he refers to Central Europe behind the Iron Curtain. What does this all matter? Not too much when you are in the US. I love to tell my friends that I am off to Eastern Europe again. But when I get over there the people I know who are citizens of these countries really, really prefer to be associated with Central Europe as opposed to "Eastern" Europe. So out of respect that its their land, I change my way of speaking. Do this and you will appear a little smarter to the locals than the typical American tourist.