I think I would like to stay here if I were a tourist and could afford it....
If you live in a city tourists like to visit, you probably have had the same thing happen to you. People call or write and say they're coming to town, and then ask you where they should stay. (Only some of them are actually asking to stay with you, and some of those, you are happy to accommodate.) And you think, "I live here. I never stay in hotels here! How on earth would I know?" But so many people ask that I thought I would post a little advice.
To stay/rent/housesit in an apartment (probably of an English-speaker), especially over Christmas or the summer, try the FUSAC website-- it's a free ad newspaper that is the biggest network for English speakers in Paris. You can also try Craigslist for Paris in English. People are often happy to have someone stay in their apts for not much money, or even free (obviously they won't advertise that-- but YOU could advertise) just to keep it occupied. If you rent, be sure and ask for references and ask the references how big/well kept up the apt is, is it in a good neighborhood, is it quiet, etc. You want to make sure the apt is not some run-down shack of a desperately poor person who needs the money. I have heard some horror stories of people finding their rental apartment had no hot water, noisy bars downstairs, filthy bathrooms, etc. Be aware that few Paris apartments have air conditioning and if the apartment is on a high floor with low ceilings, it will be very hot on warm days.
To stay in a hotel, I find Tripadvisor very useful. It appeals to all different income groups, so don't be intimidated by the expensive hotels at the top of the list. Just keep going down till you get to one with good reviews that's in your price range. I have used this technique many times to find nice hotels in various cities. Make sure the reviews are recent!
On the very cheap end, the youth hostels of Paris are quite amazing, in the absolute heart of Paris in gorgeous medieval buildings. I have checked them out several times for friends' kids and the people who stay there seem very happy with it-- plus it's a great way to meet people.
About where to stay-- Try to stay in one of the inner arrondissements if it's your first visit. The arrondissements spiral out like a snail's shell, from the center of the city, and the inner ones have low numbers like 1 (Notre-Dame) or 2. I live in the 16th, which is very bourgeois but not very central-- we are on the far western edge of the city. It's more fun to be in the center and also more practical, because after the metros stop running, you can't find taxis in Paris, and will find yourself walking a lot.
You can tell which arrondissement a hotel is in by its zip code. 75001 means Paris, 1st arrondissement, 75002 means the second arrondissement, and so on (the 75 is the département number for Paris).
My advice is not to stay in the Latin Quarter (noisy and touristy)-- on the map, the streets just south of Notre Dame-- or in the outer arrondissements-- from 9 on upward-- although of course there are great places in every arrondissement.
A couple of other pieces of advice to make your stay in Paris happier.
1) Dress up a little-- if you want to fit in, wear dark clothes. (Except-- in the summer, don't dress up too much.)
2) ALWAYS greet every single person you say anything to BEFORE you ask a question or buy something. This includes asking directions, asking store employees where to find something, buying metro tickets, getting on the bus, etc. Otherwise they will think you are rude, and might be rude back.
BONJOUR, Madame, do you speak English?
BONJOUR, M'sieu. I would like two croissants please.
BONJOUR, Madame. Which way to the metro?
BONJOUR, M'sieu. Where are the tomatoes?
BONJOUR, Madame. Two tickets please.
Also say Bonjour when you enter a store (except for huge ones) and say au revoir when you leave. Very important.
(To any older person, always say Bonjour, Madame or Monsieur, pronounced m'sieu-- it's a class marker in France and you will be treated better. You hear parents say "Bonjour QUI?" (Bonjour who?) to their kids who forget the Madame or Monsieur)
Not obeying this rule is the number one reason Americans are treated rudely in France. (Watch people ahead of you in line and you will see that every single one says Bonjour to the service person before asking anything.)
3) If you don't speak French, learn how to say in French, I don't speak French (je ne parle pas français)-- the French will find this charming and be nicer to you.
4) Most educated and most young people speak quite good English. If they don't, they'll be embarrassed that they don't. But never just walk up to someone and start talking in English. Always at least say "Do you speak English?" first.
5) If you need a French person/employee to help you, make it personal. Explain the story and appeal to them as an expert. The French love solving people's problems and will bend rules if necessary to help you. They're not as rigid as Americans. You will never hear the phrase "I didn't make the rules" from a French person!
6) In a taxi or in a restaurant, no need to leave a big tip-- just round up a bit. For example, if a taxi costs 7 euros 50, leave 8 euros. If a coffee costs 4 euros 30, you could leave 5-- but you could also leave exact change with no hard feelings.
7) Magic phrase is, "Excusez-moi de vous déranger." (Excuse me for bothering you.) This is very, very useful whenever you need someone's help, especially someone who is helping you by doing his or her job. Yes, to you it's just their job and it's normal for them to do their job. All the same, I promise that this phrase will help.