"Ahhggh", exclaimed your niece when you mentioned you'd like to see the top of the Eiffel Tower. She went to school for 3 months in Paris and assures you this is just "too touristy" for her. Well, while I agree that the lines and the crowds make this one of my less favorite tourist attractions, I say "Go for it!"  Just know that with some planning, you can make visiting Le Tour Eiffel and more of your Paris visit a bit easier. Here are a few Paris Tips:

If you want to do more than walk beneath this marvel of engineering, you can avoid the lines altogether by pre-purchasing your ticket to the top. Eiffel was a genius engineer and business man, retaining the income from the tower for his company to this day. The trick is to know EXACTLY when you are taking that ride. Your ticket is good for a 15 minute window only. Too restrictive for some -  But it may save you 3 hours of line sitting. 

I am asked all the time for help with itineraries to France. If you've been before, great! I can recommend some wonderful "off the beaten path" locations. But for the first timer, I will start by admitting there is no perfect itinerary. And, follow with, 3 days is not enough time in Paris.

That said, I offer the following very ambitious 3-Day itinerary for Paris. It assumes you will not do everything, and that this is all the time you have for the City of Lights!

First bit of advice, do some reading on being a guest in France.
For some more visit advice, see Advice for Visiting France for the First Time.