Jan
When I was in Paris, our hotel was right across the street from Gard du Nord. Walking the distance isnt terrible if you are use to walking around big cities, especially because along the river theres plenty to see, but most likely you are going to want to take the metro.
The easiest way is to take the purple #4 line towards Porte d'Orleans and then change at St. Michel to the yellow C line towards either Versailles-Rive Gauche, Saint-Quentin-en-Yvelines, Pontoise, or Argenteuil (any yellow C line heading west basically).
If you go at night, remember that the metro stops running about 1 AM, so plan accordingly. We ended up having to get off two-thirds of the way back and walking the rest of the way in the rain because the metros closed.
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It's about 20 minutes on the Metro.
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On city streets its 8.3 km as one would drive it and about 6 km as the crow flies.
You can get there by public transport on the RER B to St. Michel and then thransfering to the RER C to the Champ de Mars-Tour Eiffel stop from which it is a ten minute walk to the tower itself. The train ride takes about 20 minutes exclusive of waiting time.
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Take RER B to Les Halles, change to RER C Champ de Mars Tour Eiffel and voila! you will see the wonderous tower. Probably a 10-15 minute ride. Book Mark it-> del.icio.us | Reddit | Slashdot | Digg | Facebook | Technorati | Google | StumbleUpon | Window Live | Tailrank | Furl | Netscape | Yahoo | BlinkList