traveling in Eastern Europe as a single woman

Prague is much safer than any American city I know. Stay in center and you can walk to venues. Buses are more on outskirts of Prague. Subway and trams are in the center. Pickpockets are probably your biggest danger (let's put it in proportion- I was in Prague many times and was never pickpocketed), watch your valuables. There are many people on the streets in Prague center until very late hours. You will feel safe.

I haven't been to Budapest, but I have been to Prague, on my own, and I felt quite safe. I've also had plenty of women friends who have been there, they say the same thing. As for Budapest- it doesn't have a reputation for being dangerous. Just be aware and sensible, as previous posters have advised.
Have fun!

I traveled to Prague, Budapest and all over Croatia in October (20 days) and had no problems. I felt very safe and there were times I was out fairly late at night and also catching the public transportation 4 or 5 a.m. and had no trouble. I was mindful of my surroundings.

I am quite surprised that it's okay to walk or take public transportation even in the wee hours of the morning. I thought I'd have to stay in my motel. I'll be mindful. I'm amazed that I have so many options. If you can think of any other tips please continue to write. Thank you so much everyone. So helpful!

I agree with the other posters that Prague and Budapest are safer than just about any place I can think of in the US. That said, the American habit of smiling at strangers, whether on public transit or on the street, can be misinterpreted as an expression of interest in a more intimate acquaintanceship. So, be aware of that. Walk with a purpose, as though you know where you are going and you are intent on getting there. Plan your route before you go so that you aren't having to stop in public and scratch your head looking at a map, which is a clear tip-off that you are from out of town and perhaps vulnerable. If you need to ask directions or for information, approach mixed couples rather than solo men or groups of men. These are probably the same common sense precautions that you would observe in the US. I have traveled for years, often as a single woman, and try not to let that cramp my style, and I have seldom felt unsafe in my travels. Incidentally, you may find that you will meet other travelers in your hostel that might be interested in exploring the Prague dance scene with you. That might make things even more fun and would alleviate any worry about traveling as a single woman at night.

Great tips everyone. I will consider them all when traveling. If you have any others please keep them coming. Thank you so much.

I spent a solo week in Budapest last May and never felt unsafe.
Just take common sense precautions and you should be fine.