Paris Neighborhood for 4 Nights - 9th?

Generally fine - things can get a bit sleazy getting up towards the northern edge of the arrondissement towards Boulevard de Clichy, but the area is coming up. There may be some issues with traffic noise if the flat is actually on one of the large boulevards. No problems with public transport to the big name sites.

the center of an area defined by Gare St Lazare, Gare du Nord, and Louvre

Taking that literally, it looks like the you are talking about edge of the 9th, towards the Louvre, and the area is just fine, busy for sure but not so much in the super touristy center. It's easy to get around, and you are just about 3 km from Notre Dame. It would be helpful for people to give better answers to have a link or a cross street to reference.

The key here is selecting a rental with a significant (large) number of sincere, positive reviews-reviews that reflect a responsive, helpful attitude on the part of the owner or manager. Examine photos carefully, ask questions-then let it rip and move on. You'll have a blast.

Thank you, I appreciate your thoughts!

In case it helps, here is the link to the property/shows location more precisely

http://www.vrbo.com/862408ha?utm_source=SYS&utm_medium=email&utm_term=20150210&utm_content=propid_text_o_lprop&utm_campaign=VRBO_replyAvailable#location

The apt looks great and the location gives you access to a wide array of metro stops.
We stayed in this area 2 year ago, 2 wonderful market within a few blocks.

Looks excellent based on the listing. From the map on the listing you can figure out pretty much what block it's on, on Rue du Faubourg Montmartre. Use the "street view" feature in Google Earth to eyeball that block and the surrounding area. Looks busy but should be quieter at night, walking distance to a lot of sights and close to multiple Metro stations giving you great options for getting anywhere in the city. There seem to be plenty of places to eat, drink, get groceries, and such (which is true pretty much anywhere in central Paris). If I have the right block, there are a couple of stores selling clown costumes -- hours of fun! :-)

Thank you so much! I am now learning about the potential issue with apartment rentals in Paris. I will post another thread on that to see if I can glean some better understanding. Thanks.