+1 for Cesky Chrumlov
Also, I recommend "Student Agency" - if you are a student it is cheapest, but even if you are not, they are the best buses ever, and I don't like bus travel. It is a Czech company, but goes to many countries in the area as well as between cities. You can buy tickets online or at offices in most major cities:
http://www.studentagencybus.com/I also recommend the city of Brno. It is less crowded than Prague, and with all the advantages of a major city, but small enough to walk through. Also, the university there rents out dorm rooms by the day if you want cheap housing during the summer.
Don't know if you are planning to visit any other countries nearby, I went to Germany, Poland, and Hungary, on that regional trip with friends who went to a few other places in the region. It seems that Budapest would be another great option and is most peoples favorite, easy access while you are there.
Also, have you traveled in Europe lately? Two things have emerged from hostels that you can take advantage of, even if you are not staying in hostels.
1. The "Free Walking Tour" of all major cities, usually not too early in the morning. The gimmick is they ask for tips at the end, whatever you want to give. I've done this in about five cities and every one was top notch. It is cheaper and better than any paid for tour and perfect for your first day in the city as they will give you history, walk you around the major sites to get familiar, and give you advice like for all the cheap activities and cafes. At the end you can ask them anything. I would do this first day in any city, the next day you can do things like pay for a tour of the castle there, or go to a place they pointed out like a museum or theater they have pointed out.
2. Free Bar Crawl - you don't have to be a big drinker for this, but every evening most hostels have a bar crawl set up with deals where they take you. The main going of this is if you want to meet people and socialize. It can be cool because you tend to meet tourists from all other the world who are friendly and have tons of interesting stories.
Both of these are advertised at whatever hostel you are staying at - or if not, you can stop by and ask about them, they are happy to have anyone join.
Eastern Europe is great, and I think Czech Republic was my favorite country so have fun!