Nearing the end of my 7 months in Paris, I felt rather proud of myself. I could navigate the web of the metro without looking up from my book, knew which bakery had the best baguette and which had the best croissant d'amande, and had seen literally dozens of museums. But then I realized all I had yet to experience...the pieces of the urban puzzle unexplored, the food not yet tasted!! But after an uncomfortable moment or two I realized -- it's just this, this unending nature, which give Paris its character and its charm. The anitiquity is coupled with an ever expanding and cutting edge atmosphere - one can never see it all.
Take some daytrips - the train ride is beautiful no matter what direction you branch into. Giverny, Reims, Rouen, Tours, Chartres, Deauville... all are well worth it.
Maison Kayser is arguably the best bakery in Paris -- eat there as often as possible.
Stroll the Ile Saint Louis.
Quick Tips:
Go take in the view from Georges (in the Pompidou Center). Sit with a coffee and watch the movement of the city below.
All of the hidden museums that one never hears of are interesting and quiet -- check out the Delacroix Museum, the Musee de la Vie Romantique, the Maillol Museum...etc.
Also - every exhibition in Paris is incredibly thorough and well-done.
GET PARISCOPE to see what's happening in town!
Take the Metro as much as possible.
Avoid the heavily touristed areas in the summer.
Explore each of the markets - they all have something unique to offer.
Bring "Hemingway's Paris" with you -- it has great walking maps which bring you past the former haunts of the artists of the 20's and 30's.
Walk all over -- it's the best way to discover small boutiques and cafes which aren't listed in guidebooks.
Best Way To Get Around:
The Metro (only until 12:30 am).
Walking -- you'll discover much more than you'd ever find listed in a guidebook.
You may want to get some walking guides in whatever genre you're particularly interested in.