There were 36 three bedroom homes that sold in Hamilton over the last year. They ranged in price from $125,000 to $900,000. 16 of these homes were built between 1950 and 1970. This subset is what you will probably want to look at to determine the value of your home.
The least expensive sale in this subset was 2 Village Lane which was a three bedroom one bath ranch which sold for $190,000. The most expensive was 14 Griffith Road which was a three bedroom three bath cape which sold for $729,000. To figure out exactly where you house falls within this range I'd need some more details.
You could also take a look at three bedroom houses currently on the market in Hamilton (see link below). If you can apply an unbiased eye you can probably figure out how your house matches up to these and price it slightly higher or lower as is appropriate.
My best guess is that you should probably be in the mid $400,000 range.