As a Frenchman, I have been invited to give my opinion about the meaning of "Pont Neuf". It must definitely be translated as "the New Bridge", though "9th bridge" is gramatically correct as well. Remember that all bridges on the Seine were named by historical reasons, and, dating back to the 17th century (as judiciously mentioned by protomartyr), "9th bridge" would have been called "Neuvième Pont" and not "Pont Neuf" (Name + number is more likely to be found now in modern technology: terminal 3, section 2, etc...). I acknowledge that Harold's translation is relevant as well, though not correct in this case ("new" can be translated by "neuf" or "nouveau" according to the contexte).
I hope your next trip to Paris will allow you to discover the history of its bridges. My last advice: when in Paris, buy 'L'officiel des spectacles': it is a very cheap weekly book (published every wednesday at a price of 2 or 3 FFr) where you can have a lot of information about entertainment, food and night life with comments and price. There is a section about Paris events where you can find cheap Paris tours with retired guides or volunteers. This may help to perceive a true Parisian touch...