If you live in a city you should be able to access the water report and they usually report the amount of residual Chlorine at the tap. A lot of my early brews had that "taste" no matter what style I was making. I have found that it is really important to control fermentation temperature, ensure that the wort is aerated properly (if using liquid yeast), and pitch the proper amount of yeast. Go to mrmalty.com or yeastcalc.com for proper pitching rates. I would start with these 3 things before investing in a water filter. There are also ways to eliminate Chlorine from your water that you can do a search on if you just want to make sure that is not the problem.