Try as many bikes as possible. That Bianchi mentioned above looks to be a really nice bike. Somehow you just can't go too wrong with a Bianchi. Other bikes in this price range (~US$600) you might want to check out include:

• Jamis Aurora
• Specialized Allez 24
• Trek 1000
• Trek 1000C (comfort version of 1000)
• Giant OCR3
• Fuji Finest
• KHS Flite 300
• K2 Mach 1.0
• LeMond Nevada City - although this bike is a bit more than your budget, you may be able to find one on sale or clearance/closeout. I felt that it's a pretty nice riding steel frame for its price and had to be mentioned.