Sorry for the late reply, I totally missed your post.
The obvious and spectacular spot is the Trocadéro, as the fireworks are usually launched from the Eiffel tower, but as you said the place will be probably be packed.
There are many other spots though. Look at my gallery, I have two Eiffel tower pictures with the locations described in the comments.
The right bank of the Seine is full of good spots, and you also have a nice view from many bridges around the tower: Mirabeau bridge, Bir-Hakeim bridge, passerelle Debilly (don't miss the Quai Branly museum if you cross this pedestrian bridge).
Or if the weather is good, simply in the Champs de Mars park behind the tower, so you'll have the Trocadéro in the background.
A good way to explore in advance is to use the Street View in Google Maps