Most of the important things were already written, but I would still like to add a few sentences as I have spent 6 months in paris and know the city rather well...
if you visit notre dame, then also visit the tower as you will not only have an excellent view over paris, but you will also see the gargoyles that are really impressive to see.
if you are interested in graveyards, you better go to the montmartre graveyard which is a little smaller than père lachaise, but much nicer and quieter and you will still find a big number of famous ppl there.
also sacre coeur is really worth having a look, you can also climb up the tower and have an excellent view over the town. rather spend your time here than on the tourist trap place du tertre...it has nothing to do with the romantic impression you get from seeing it on tv, it is horrible!
what many ppl dont know: have a look at the old opera house, sure entry fees are not very cheap in paris, but it is worth it....the interior is made of marble, mirrors, etc.....if you are lucky, you might even see the phantom :)
the conciergerie is not too impressive, you better save that money and also save the money for la chapelle which is found near notre dame on the ile de la cite...it is definitely too small to pay that much money for it....if you have time, better go to st.denis - there you will find a very beautiful church with the tombs of all (or almost all) french kings and queens....its impressive!!!
dont spend to much time on the champs d’ellysee, because it is full of expensive shops and restaurants...if you are into shopping, try the shopping centres at les halles or la défense...
about the eiffel tower, you dont need to go to the 3rd floor because it is overcrowded and the view is also good from the first floor which also provides you with a lot of information about the tower and the town....
hmmmm..that is all so far, e-mail me if you have questions....