Agree with kimd - Arc de Triomphe is better than Eiffel Tower. You get amazing view of the Etoile and right across the city.

Take a river trip on a Bateau Mouche, either by day or in the evening with a meal included. Very romantic.

Lots of nice designer shops and lovely cafes in St Germain des Pres area - Cafe de Flore esp good.

Musee Rodin is amazing, and free to get into the gardens where many of Rodin's most famous works are on display, like 'Gates of Hell' and 'The Kiss' for example. A little oasis in the heart of the city.

Buddha Bar is great place to people watch at night, or ManRay, just off Champs Elysees.

The Conciergerie is also pretty amazing - you can see the cell where Marie Antoinette spent the last days of her life before being carted away to the guillotine!

Pompidou Centre is another fabulous (modern) art gallery.

Best evening's entertainment is without doubt the Lido on the Champs. The most beautiful girls and best acts.

Paris is a very easy city to get around, either by metro or on foot. It's fairly compact, so if the weather is good, make sure you're wearing comfortable shoes and just take your time and stroll around. You'll see and experience so much more, and just stop at any pavement cafe for a delicious cafe creme or chocolat chaud and watch the world go by! Honestly, there is SO much to do, you won't be bored for a minute. And just to repeat the warning, pickpockets are EVERYWHERE on the Metro, esp. line No 1 - so be vigilant.

Have a great time!