Most basic test you can do on your tap water is go to Wal-Mart in the Automotive/RV section and pick up a TDS meter for $12 to test your water. If it is below 100 it is probably good for fish only, if it is below 20 it is probably good for reef. I have never seen water from the tap ever have numbers that low though.. think the lowest tap water TDS I have personally seen was around 190.
Personally I wouldn't risk tap water on my tank, but to each their own. Heck, I even tried what is considered "good" natural sea water that is pulled in from out in the ocean thinking "it came out of the ocean, from a pipe about a mile out it has to be good" Nope, it still had phosphate levels through the roof, alk was low, and there was almost zero buffering capability of the water (B-Ionic dosing didn't do much at all for Alk, it would raise the pH to dangerous levels and still not get a DKH any higher than 7). All I got out of using water out of the ocean was bad cyano outbreaks and hair algae explosions, similar to what happens when you use bad tap water.