http://en.wikipedia.org/wiki/Saint-Eustache,_Paris

I found it by accident and it was really impressive. Didnt show in any of the brochures etc.

Recommending the trip by boat around the city, its not super awesome mega amazing, but its worth it. I think it was about 10E per person.

The Louvre has a free day, i think thursday. Depends on what you want, one year i went then and it was way too crowded. Other year I went and payed and enjoyed it much more. Not sure if teh free day was soemthing special or if its all year around.

Versailles is about 45mins by train. It wasnt much of a hassle to get there and I dont remember the train being expensive. If you have an extra day its worth spending it on that, otherwise no.

Subway system is pretty good, didnt have much problems except for the day of the republic when it was so crowded we decided to walk an hour instead of taking it, but youre not there for it. I remember soemthing about getting a week ticket and that it was cheaper but I dont remember how much it was or where I got it.

Best ice cream is on the smaller island. Youll recognize it by a long line of people.

Edit: as for the eiffel tower, i didnt go up on it but it was a good sight from the bottom due to the metal construction thingy. I dont know if thats interesting for you but id say its worth the trip. Theres the mars field next to it which is just a big park but its nice.