We have done a lot of walking in Paris. I was impressed by L'Defense, the very modern high rise area to the west. It includes the Grand Arch which is aligned with the Arc de Triumphe and the Champs Elisee. Also, the Montparnasse building to the south give views similar to the Eiffel Tower with much shorter lines. Also: Gallop France at the Hippodrome - a free horse racing event (don't know the dates). Street markets, sidewalk restaurants. Versailles palace.
Definitely check out the Monteparnassus Tower. It's the only tower that you can get pictures with the Eiffel Tower it. (smile). It was well worth it. The views were great. I just couldn't stand in the long line for the Eiffel so Monteparnassus was a great substitute.