How to properly filter water to drink? Trying to cut costs down.?

How do I properly filter water? I live in NYC. Supposedly the state of New York, or NYC has one of the cleanest water in the country. I basically boil the water from the sink and then let it cool before I leave it in the refrigerator. Any tips I can better improve the taste or filtration of my water? I have a little weird water taste while drinking it, but it taste like water foundain. I read water in bottles, they add some chemical to remove that iron type taste. I just want to make sure I am drinking healthy and clean water. I do not want to buy those filter thingy to filter my water because I would have to keep replacing it. ANY TIPS? THANKS!