Paris city, Known as the "city with a 100 villages", Paris is divided in 20 districts (known as arrondissements).
The Paris subway (Metro) is exceptionally fast and clean, it may be your preferred means of transport while in the City of Lights, and all hotels in the center of the city are at a walking distance to a subway station.
Although there is a fine Metro in Paris, I really recommend a shared shuttle service or a VIP private shuttle service, and by far the best of them all is Always Shuttle, really good transportation from and to Paris city.
Always Shuttle have English speaking drivers, a necessity in French speaking Paris... you will find that using such transportation is by far cheaper then taxi and much more efficient, since you get to your destination on time, and in reasonable price range.
Since it is impossible to define where the center of Paris is, the best is to choose your destination according to what you'll want to do and which ambiance you want to experience during your trip.
The Right Bank with it's best toured areas, who are filled with monuments, museums and shopping areas:Louvre - Les Halles - La Bourse
Ope'ra - Madeleine
Le Marais - Ile St Louis
Champs Elyse'es-Etoil
Trocade'ro
Montmartre
I'd recommend these areas to stay in, and you can easily find all ranges of accommodation in the areas I specified above. From the most expensive ones to the low budget hotels.
Enjoy Paris! And don't forget my tip regarding private shuttle services such as Always Shuttle, they are the best in this area!
by the way, I really recommend a very good Paris airport shuttle - alwayshuttle.com, clearly the best transport to Paris city I have ever seen!