The best view of the Eiffel Tower
Place du Trocadéro, 75016 Paris (Map)
I often seen tourists looking at their map and discussing which Métro stop is closest to the Eiffel Tower so they can get to it as directly as possible. This sounds perfectly logical, but I always tell these people they're making a mistake! If you take the Métro to one of the stops that's closest, you exit into a boring neighborhood, you can't see the Tower from where you are, you don't know which way to go, and the whole thing is pretty anti-climactic. But there's a much better way!
Take the Métro to the stop called Trocadéro, on line 6 or 9. In the Métro station, follow the signs toward the exit marked "Tour Eiffel." Walk up the steps to the sidewalk, and walk forward ten meters or so, and on the left there'll be large open square with a few steps leading up to it. This is the Place du Trocadéro. As soon as you arrive in the Place you'll be greeted with an absolutely breathtaking view of the Eiffel Tower! (Note: in recent months there's been a temporary wooden structure partially blocking the view when you first arrive on the place, but you can walk around to the side of it to get the same great view.) Here'll you'll find all the other tourists who got this same advice from someone. The Place du Trocadéro is THE perfect place to get the best possible photos of you and your entourage with the Eiffel Tower in the background. You'll see lots of people putting their arm out and lining up the pic just right so it looks like they've got their hand on top of the tower; give it a shot! This is very possibly the place where you'll take the photo that defines your visit to Paris.
Now, as for actually visiting the Tower, you're in for a beautiful stroll. The Place du Trocadéro is just on the North side of the Seine (that's the river, duh), and the Eiffel Tower is just on the South side. There's a bridge directly in front of the Place du Trocadéro that'll let you walk over to the Tower; you'll just have to go down the stairs in front of the Place, and cross a very busy street (wait for the "Walk" light!). It's a fifteen-minute walk from the Place and over the bridge, and you'll be treated to a wonderful view of the Tower as it gets larger and larger in front of you. I've often said, most world famous monuments are disappointingly small when you see them in person, but the Eiffel Tower is amazing in that it's bigger than you expected it to be! It's really fantastic; be sure to take a moment to marvel at this metal giant and wonder at how it was put together by human beings in the 19th centry.
In the Place du Trocadéro and during the stroll down to the bridge and over, beware of the dozens and dozens of guys walking around selling Eiffel Tower souvenirs. They can be a bit pushy, but they're never mean or dangerous or anything; they just really want your business. Repeat the mantra of "Non, merci" over and over again to each of these guys as they approach, and they'll leave you alone; just be firm but polite and you'll have no problem. If you're lucky, you'll get to be there when a bike cop shows up and all the souvenir guys gather up their wares and run like hell! Exciting!