Which arrondissement??

Looking at Rick's Planning Map of Paris, those arrondissement would be (in approximate order of my perception of the apparently popularity with travelers here, but not trying to speak for others):
7th, 6th, 4th, 5th, 3rd, 2nd, 1st, 8th, 9th

All of these arrond. meet your basic criteria. However, for selecting a Paris hotel, the neighborhood matters, as well as the arrond.

Maybe subsequent posters will mention their favorite neighborhoods in which to sleep.

Anything from 1-9 will be very close to all the sights. One very nice thing about Paris is that central Paris isn't that big and all the sites are pretty close together. The Metro is also amazing and will get you everywhere quickly.

Many advise to be as close to the river as possible After having been to Paris several times, if I were a first timer, I'd pick the 4th, 5th or 6th. Ibkmow some who advise first timers to stay in a hotel rather than an apartment so as to have the assistance of the hotel staff. You might search "apartment hotels" on www.booking.com and see what comes up.

Check out a book "An Hour from Paris." It has details of many locales that can be reached from Paris within am hour or so by train. Gives instryctions on how to get there and telks what you'll see when you are there.

BTW, many neighborhoods in Paris are like small villages in themselves, so be sure to leave plenty of time to wander around Paris.

We stayed in the 7th ,close to the metro , walking distance to the arc de triomphe . It was our first time there in 2013 , get a map of the metro and you can go to any district and enjoy all the sights and walk around and enjoy the cafes.

Really almost anywhere close to a Metro station (preferably a station where two lines intersect) will be fine. Closer to the river means more sights in walking distance, also more expensive. We had a great time in the 14th a couple of blocks from the Pernety station. There are street markets, grocery stores, nice restaurants, "traitteurs" (ready-cooked food, mostly Asian), etc. everywhere.

If you're scoping out an apartment to rent, on homeaway.com, vrbo.com, airbnb, or whatever, use Google Earth to find its approximate location and the "street view" feature to eyeball the neighborhood.

I think Kent has it about right for arrondissement popularity on this board. The 7th is popular, in part, because it includes Rue Cler which RS recommends. But there are many similar areas in Paris. One advantage of an apartment is the potential to live in a more "real" neighborhood with French neighbors and non-tourist-oriented businesses. Anyway, it's hard to make a mistake on the arrondissement.

Carolyn's recommended "An Hour from Paris" may be a fine guide, but I'd hate to be staying anywhere near that far out of town and have to spend all that time and money commuting. Might be very useful if you're looking for an affordable place to live and commute to a job, but not so much for the sightseer, I'd think.

I would not focus on arrondissements so much as I would focus on trying to find the right neighborhood. Take a look at https://www.airbnb.com/locations/paris/neighborhoods and see if you see neighborhoods that you like. If the neighborhoods are in the 1st through the 9th, chances are they are close enough for you to walk to some sights.

We rented an apartment in the 3rd arr. in 2012. It was very convenient for walking and for metro access. There were 2 "supermarkets" within a few blocks and Le Marché des Enfants Rouges was almost across the street. There are lots of areas like this, as has already been mentioned, just waiting for you to enjoy them.

I recommend that you get a copy of Streetwise Paris, either from the RS online store or maybe your local bookstore. It was our map of choice. It shows just about everything you need to know in an easy to read and compact laminated format (about the size of a legal envelope) with a street index, metro stops, major sights and more. The arrondissements are also marked.

Combining it with the Google satellite option and street view recommendations will help you to pick a location. My husband and I stayed in the 7th our first trip, and a friend and I stayed in the 8th (I think) on my very first trip to Paris. That was a very long time ago. Anyway, I much preferred the 3rd precisely because it felt more like a real neighborhood to me.

Wherever you stay, you will have a wonderful time.

Sorry, I accidentally posted my comments about the book "An Hour from Paris* to the wrong thread. Don't know how I managed that.

Thank you to everyone! We still have a lot of reasearch to do, but these replies make it seem as if we can't go too far wrong. I appreciate everyone's thoughts!