white vinegar has always worked for me and I ask people if they smell any pet odors when they walk in. They always say no.....so I think it works and is a lot cheaper than some of the products out there.
I haven't gotten a new puppy yet but I have a 7 year old dog. We haven't had any accidents in years of course but recently I was in Petsmart and saw this stuff for "hard wood floors" it was specific to clean hardwoods for urine. I think it was a natural cleaner that took out the urine smell and was safe for hardwood.