It is quite simple: Coffee is at least 98% water; therefore, the higher the quality of water, the higher the quality of the resulting cup of coffee. If your tap water tastes good at room temperature tap water is probably fine for making coffee. If your tap water has off flavors, then your coffee will have off flavors. Many people use filtered or bottled water for their coffee. There is a difference.
Some of the newer more expensive coffee pots come with replaceable charcoal filters built into the machine. If at all possible don't use distilled water. It is missing minerals that make water pleasing to drink. Please note that your taste buds are more acute when tasting warm liquids so it is important to taste your perspective water at room temperature since you will be drinking your coffee warm.