Caroline, almost everyone would agree that, on the whole, Paris is one of the safest big cities in the world. But, like all big cities, some parts of it may "feel" less safe than others, especially at night. Regarding the 15th arrondissement, it is so large that your hotel could be very near ... More on tripadvisor.com

If you go near Moulin Rouge, do not cross the road or you might end up on the dangerous 18th, instead of safe 9th. Some tourists even reported weird people painting portraits of them there. More on reddit.com

I've spent ~7 months in Paris and here are my thoughts: Montmartre is not at all "the outskirts" of Paris, but it's a hike uphill to get to the middle (and the metro Abbesses has a million flights of stairs). This means it takes much longer to walk and metro to central Paris and the main tourist sights. The areas between central Paris and Montmartre can a little sketchy at night. St. Germain is an upscale neighborhood, has lots of cute restaurants and is very central. You may find it too touristy. Boulevard St. Germain has all of the fancy designer shops and can get pretty crowded, but I love the area right below Boulevard St. Germain by Mabillon/St. Sulpice. There are some little streets there with really cute bars and restaurants that don't feel as touristy. I personally would recommend the northern part of the Marais in the vicinity of any of these metro stops: Republique, Temple, Arts et Metiers, Filles du Calvaire or even Oberkampf/Parmentier. Rue de Rivoli in the bottom of the Marais is full of tourists, but the area to the north is much better. From this area you can get anywhere on the Metro or by walking (for example, Place de la Republique to Notre Dame is under 30 minutes walking and straight through central Paris, totally safe and a nice walk). Some parts of this area may seem a little hipster but definitely not to the degree of Bushwick. At night, you can go further north into Oberkampf or Belleville for the hippest bars and restaurants. More on reddit.com

Obviously no neighborhoods could be sum up in only a few sentences but I hope I can give you a somewhat accurate and succinct description of each arrondissements : 1st : Most of the arrondissement is just the Louvre and the Tuileries garden. Lots of bars near Chatelet, big shopping mall in Les Halles. It gets posher further west with the Palais Royal and the Place Vendome. Not a whole lot of people actually live here. 2nd : The smallest arrondissement. Rue de Montorgueuil is known for its many restaurants and food places. Trendy bars and concept stores around Etienne Marcel/rue Tiquetonne. It gets livelier to the north along the Grand Boulevards. 3rd : the north of the Marais. Lots of museums, somewhat touristy but relatively quiet with narrow streets lined up with various kind of shops. 4th : south of the Marais. The Jewish and gay neighborhood. Used to be slummy and working class, it's now completely gentrified. Often crowded, with clothing stores basically everywhere. Île de la Cité is pretty much just tourists visiting Notre Dame. Île Saint Louis is a millionaire ghetto. 5th : The student neighborhood, with a large number of prestigious universities. As rent rises and book shops closing down, the place is slowly losing its student town vibe. Very crowded and touristy to the north near Saint Michel, a bit quieter as you go southward. Still a lot of student bars in the small winding streets around the Pantheon / rue Mouffetard. 6h : Saint Germain des Prés, to the north, used to be famous for its cafés, vibrant nightlife and jazz clubs, but it's not really there anymore. Still quite a lively neighborhood around the Boulevard St Germain. Most of the southern part of the arrondissement is the lush Jardin du Luxembourg, the area around it is a bit quieter. 7th : Lots of administrations, embassies and government agencies. Really really wealthy and boring. The Invalides and the Eiffel Tower are there, though. 8th : Luxury brands and five-star hotels around the Champs Élysées, massively touristy. Much more tranquil but still very rich around the Parc Monceau. Mostly offices and high end clothing stores around the Gare Saint Lazare. 9th : near the border with the 8th, a lot of offices, banks, restaurants and Grand Magasins (Galerie Lafayette, Printemps). It gets a lot more grimy (but more fun ?) as you go north near Pigalle and Anvers. 10th : Mostly occupied by the Gare du Nord and Gare de l'Est railways stations. Somewhat shady at times. Quite hipsterish to the east around the Canal Saint Martin. Lots of afro hair salons on the Boulevard Sebastopol and Magenta. 11th : Basically a hipster utopia. Former working class neighborhood now filled with trendy bars and restaurants, especially between Bastille / Faubourg Saint Antoine / Oberkampf. The north is more residential and less gentrified. 12th : Quite quiet, some might say boring, especially to the east and south. Mostly residential. It gets more lively as you approach the 11th arrondissement and Gare de Lyon. Big ass park in Bercy. It's also bordering the Bois de Vincennes. 13th : Lots of tower blocks and modern architecture. A brand new area has popped up in the last decade near the Seine river (ZAC Paris Rive Gauche). Large Chinese and Vietnamese neighborhood (triangle de Choisy). Some small and quaint areas sprinkled throughout like Butte aux Cailles and Les Gobelins. 14th : Some consider it boring, some think its still a living remnant of a more authentic Paris. Gets quite busy to the north near Montparnasse but it's essentially residential. The Catacombs are underneath it. 15th : Many think of it as a family neighborhood. You may find some activity around rue de Vaugirard, rue de la Convention but it's true that's it's not as crowded as the rest of Paris. 16th : Wealthy and posh. People may think you're basically a bourgeois scum if you live there. Not much to see there apart from the Trocadero and some nice early 20th century architecture. Bois de Boulogne to the west. 17th : Pretty much entirely residential. The northern part is a bit poorer than the southern one. A brand new neighborhood has been built there around the Parc Martin Luther King. Some activity near Place de Clichy. 18th : Montmartre is almost a Parisian Disneyland at this point. Completely different vibe around Chateau Rouge. Barbes is well known for its East-African Market, it's also steadily getting gentrified. Further east the neighborhoods of La Goutte d'Or and La Chapelle have always been some of the poorest in the city and it still holds true today. 19th : Lots of big tower blocks to the north of the canal. The area around the bassin de Vilette is quite trendy these days. The Parc de la Vilette to the east is home to a number of museums and concert halls. Some quiet areas near the Parc des Buttes Chaumonts (Buttes Bergeres, Mouzaia). Traditionally working class to the south, in Belleville. 20th : to the north the Belleville/Ménilmontant neighborhoods have also been some of the poorest in Paris. The area is undergoing gentrification with some art galleries, nightclubs and coffee shops popping up, especially around the Parc de Belleville. The rest of the arrondissement (Pere Lachaise, Charonne) is a bit more sleepy and residential. More on reddit.com