That is an interesting question and one which deserves some answers. The short answers are, yes black holes do travel just like anything else and yes, our earth and solar system most certainly are being attracted by a black hole. But there is no need to worry, we are not in danger of falling in any time soon.

Black holes can travel around and orbit other bodies just like a star or a planet. Black holes can even collide and create bigger black holes. As a matter of fact, it is now thought that most galaxies orbit around what are called super massive black holes. This includes our own Milky Way Galaxy. But like I said, three is nothing to worry about. Our solar system is orbiting this black hole, not falling towards it. So technically we are being attracted to it, the same way the earth is attracted to the sun, but there is no danger of falling into it any time in the foreseeable future.

To answer your question, yes, black holes move just as any other stars in the galaxy; it is subject to the same gravitational laws as any other bodies so it does attract masses and it is also attracted by other masses.

From what I've read, our sun isn't large enough to become a black hole itself. I think there is a possibility later on in the very not near future that it is possible that Earth could come into contact with a black hole. It's possible, but not something we need to worry about as it would probably happen way after humans are extinct.