Frankly it doesn't really matter where you stay in central paris (the first 10 or so arrondissements by #), as long as you are close to a metro station.
When teenagers in Paris call each other on their mobiles to arrange to meet, the meeting time is alway "vingt minutes", as it takes no more than 20 minutes to get to anywhere from anywhere in central Paris via the Metro.
If any major city has a better public transport system, I have yet to see it.
Now London, on the other hand....the public transport is so awful that more and more Brits look to move elsewhere to avoid the ghastly commuting and overheated property prices....Edinburgh, anybody ?