What facinated me was that in different parts of the city, you could see the tower because it is so high. So every change I had, I would make a picture!
View on top of the department store Galerie Lafayette
View from the Louvre museum
But please don't think that it is romantic when you're by the Eiffel Tower... Unless you think that groups of children standing in line to go up the tower and making a lot of noice while men trying to sell cheap souvenirs and coming up to you every 30 seconds is very romantic. But still, something that you need to go and see for yourself!