A few website options for your consideration:
https://www.google.ca/search?q=apartments+in+hamilton&aq=f&oq=apartments+in+hamilton&aqs=chrome.0.57j0l3j62l2.4170&sourceid=chrome&ie=UTF-8
There are good and bad areas of Hamilton, like any other city. I am actually from the area (undergrad at Mac!), so I'd be happy to offer further advice. Generally speaking, you want the west end of Hamilton. I'd suggest looking no further east than James Street and no further north than King. Westdale is an area where any street is good.
Hope this helps as a starting point.