Going to the Eiffel Tower, Yes, do get there early. We were there a few years ago and made it up in one of the first groups. By the time we came down the line was extremely long. We did also do a lunch on the deck level at the fine restaurant there. No reservations, but were there early enough that they fit us in. Champagne, French Onion Soup, Cheese (Formages) and other goodies. It was memorable.
http://www.eiffel-tower.com/
The French do frown upon Blue Jeans. Try to bring along some black pants or something a little nicer. You will get a better reception.
The Musee d'orsay is an excellent museum right across the river from the Louvre. Many of the Impressionists paintings. Whistler's Mother painting is there also. Worth checking out:
http://www.musee-orsay.fr/en/home.html
If you get a chance to go to the Palace at Versailles, do it. There is a train that you can catch near the Eiffel Tower to get you to Versailles. Try to get there early. It was very cool to see the Hall of Mirrors with no one in there.
http://en.wikipedia.org/wiki/Palace_of_Versailles
Public transportation will get you all around, but you will also do plenty of walking. Check the site for some good deals on subway passes and museum tickets.
http://www.parismetro.com/
Sacre Coueur is worth the trip also. You can see it from the city off in the distance on the hill. You will also be up near the Moulin Rouge. Not the best neighborhood at night but maybe they have cleaned it up some since we were there.
http://www.paris-tourist-information.com/sacrecoeur.htm
Do visit Notre Dame. The trek up to the bell tower and the gargoyles is worth doing.
http://www.notredamedeparis.fr/-English-
While on the island also visit the smaller cathedral, Sainte-Chapelle
http://en.wikipedia.org/wiki/Sainte-Chapelle
Do take a river cruise whether it be during the day or at night. We did it at night it was very enjoyable seeing everything lit up.
Another thing to do is to go the department store La Samaritaine. There is a deck at the top where you can get a great view of the city. And it is FREE. Take a look around in the store also.
http://en.wikipedia.org/wiki/La_Samaritaine
Visit the arc de triomphe it is worth going to. Don't try to cross the circular street around it. There are tunnels that go underneath the street. You can walk around it and can pay a fee to go inside and go to the top. It's a fun thing to do.
http://en.wikipedia.org/wiki/Arc_de_Triomphe
Just down the street is the Lido. The shows there are pretty good.
http://www.lido.fr/us/cabaret-paris.html
Stroll along the Champs-Elysees, many great restaurants.
Have a Great Time!!!