Probably the most desirable neighborhood to live in Paris would be the area around St Germain.
There are three famous old places to eat:
The Alsatian Brasserie Lipp,
Cafe de Flore,
and Les Deux Magots.
All three with their old-school formal waiters, trendy Armani wearing crowds, families of tourist and locals alike.
All three are cemented right outside Saint-Germain-des-Prés church:
For an avowed atheist, I surely end up going into a lot of churches. I like them. They are usually quiet places and full of history, two things that really appeal to me. This one is no exception. It was founded in 558. Really! Some of the pillars inside are the original, 1500 year old stone pillars. The church survived lots of fires and rebuilding and wars and plundering over the century. The bell tower is the oldest in France- that was finished in 1014.
It's amazing to have something so grand and old that you can just walk in and check out.
A quick walk down the street brings you to one of the most treasured gardens in Paris- Jardin du Luxembourg. Marie de' Medici, homesick for her native Florence, had the palace gardens laid out in the style of her homeland.
A walk up the hill through the Latin Quarter brings you up to the Pantheon, where notables such as Marie Curie and Victor Hugo find their final resting spot.
For a millennia, this has been the area where the universities of Paris have been. The language of the educated was Latin, hence the name, and the area is still flooded with students and great places to eat cheaply. At night, the neighborhood comes alive with music and drinks and dancing.