If you strike out from the Île de la Cité (pictured) in Paris and walk along the left bank of the Seine, you’ll eventually hit a district known as the 13th arrondissement. It'll take you a while (about 3/4 hour) but will give you a chance to discover places those well-travelled friends back home may not have seen. And if they have, good on them – most visitors to Paris don’t seem to venture far from the Champs Elysees. I know someone who hardly strayed from the outer walls of his superbly-located hotel, as he found the city too daunting to tackle on his own. Yes, it’s unfathomable, but there you are.
Photo by Rita Crane Photography
To be in Paris and not go sightseeing is a criminal offence, whereas not exploring the 13th arrondissement is entirely understandable, as it isn’t yet part of the tourist trail. However, things are happening there: take a look here for ten nice reasons to go. And here are some more: a walk through the quaint La Butte aux Cailles “village within a city” and a look at the amazing, ultramodern Bibliothèque Nationale de France or BNF (don't miss Louis XIV's gorgeous globes; pictured). 
Wikitravel has the lowdown.
Photo by photogestion
Now, a confession. You don’t really have to walk from the Île de la Cité, which is a place you must under no circumstances leave Paris without seeing. The 13th is quickly and easily reached by Metro from stops around the city. It’s just that a stroll down the Seine will be much more rewarding. Unless, of course, you’ve chosen the wrong footwear (always, always, ALWAYS think comfort in this city), or you’re my agoraphobic trainee travel agent ex-friend.
When you've had enough of life in the 13th, cross the Seine from the BNF on the elegant Simone de Beauvoir footbridge (pictured). It'll take you to the Parc de Bercy - a place that's full of surprises.
Tout alors. Au revoir.
Photo by mistinguette18