Graz is great, I went to Graz and Vienna a few years ago. Austria in general is really nice.

In Graz I loved this bar/coffee shop called Aiola Island that sits in the river -
http://www.xomba.com/aiola_island_is...licious_coffee
it was really cool!

Make sure to get out and about and see other places in Austria too - their railway system was really smooth and efficient, made it very easy to get to Vienna, I'm sure other cities are easy to get to.

Here's a fun fact - Arnold Schwarzenegger was originally from Graz. They named the local sports stadium after him, but I think the name has been changed now. It was still the Schwarzeneggerstadion when I went there though (I went to see Scotland play Austria at football/soccer).