I am visiting a friend for a week in Bilaystok, as this is my first experience with Poland, I am quite nervous!
What is there to do in such a city? Also, how safe is it for a foreign woman to be walking around alone at night, etc?
Białystok is a cool town. There are quite a few things to see in the city and in the countryside. Whatever you do, make sure that you attend the Sunday Divine Liturgy at St. Nicholas Orthodox Church. The choir is one of the best in Poland, and it is definitely worth seeing. The service and music are breathtaking.
The Holy Spirit Orthodox Church is also a gem.
There is a really interesting Medical Museum that is worth visiting, too.
You will be safe as long as you avoid drunken people. Threats to personal safety almost always come from drunken people in Poland, so if you avoid them, it is highly unlikely that you will have an unpleasant experience. Don't worry. There are lots of students in town, so you will have no problem finding people to talk too. You'll have fun!