Prague - one of my favorite cities and I've had the good fortune of teaching a 2-week class there 4 or 5 times. Make sure you take a late evening to walk across the Charles Bridge. You get a great view of the royal palace all lit up and the street musicians and performances are wonderful. The same trip during the day is also lovely with many vendors and street musicians on the bridge. There's many great places to eat Czech food on the old town square - you'll have to get the svíčková at some place (marinated beef with a heavy cream sauce, served with a side of thick, stick to your ribs dumplings and a little dab of cranberry sauce). Match it with a good czech beer (try the original Budweiser - no relation to our crappy beer). I ate many a time at "Staromestska Restaurace (Old-Town Restaurant) on the Old Town Square. It's a light greenish building on the south side of the square, on the signs, next to the name of restaurant, is a Pilsner Urquel sign. Good food, authentic Czech, reasonable prices.
The astronomical clock tower is a must see but it will be crowded with tourists. It's worth the time and effort to wander up to the Petrin hill observatory and then wander back down through the old apple orchards below the monastery. Lovely views of town. On the way up, you can visit Prague castle. Also, if you have the time, take one of the river cruises.
Of course, be careful with your wallets and don't be surprised if the beautiful tourist areas you visit during the day (in particular the Wenceslas square) are a bit seedier at night. Multiple ladies of the evening will appear hawking their trade in a somewhat aggressive manner. Walking as a couple, you'll most likely be left alone, but a single guy walking around at night is a target for these gals. PM me if you want ideas or other information about Prague.
