What do see really depends what sort of thing you like doing of course.
Yes, the Louvre and D'Orsey but the Musée Marmottan-Monet is the museum dedicated to Monet if that's the sort of thing you are interested in. Also, the Orangerie (which is at Tulerie) is the home to some of the biggest and most famous Monet waterlily works. There's a permenant exhibition there too, small but interesting.
Also there's the Musee Rodin at Metro Varenne. They've done it all up fairly recently. It's particularly nice in the summer though as the garden is one of the main attractions.
Invalides is another place you might like to visit. It's Napoleon's memorial of course so his tomb is there under the dome, but there's a pretty good collection of military armour.
Someone mentioned St Denis and the Basilisc and it is nice when you there to spend a bit of time wandering around Montrmatre which was the drinking ground of the impressionists and is a network of little cobbled streets with cafés and outside tables.
Someone also mentioned St Chapel and I agree, the windows are magnificent.
A tip about the museums: it's best to go online and check they are open. They have a habit of shutting at odd times like Tuesdays I think, and you can actually book a slot for exhibitions online so no queueing.
As for tips, well one of the nicest ways to get to the Tour Eiffel is to go to Trocodero (there's a museum there too I think photography from memory) and from the terrace, you get the best view of the tour. It's the real tourist view where you can have your picture taken with it in the backgroud. You can then walk down through the gardens to the tour (it's about a 15 minute walk though). The tour is a bit of a pain to get to on public transport anyway so it's quite a nice thing to do s Trocadéro is not far from the Etoile.
Another tip is starting at the Etoile ( Arch de Triumph) you take the bus 92 from Avenue Marceau. It goes right though the heart of Paris, around Concorde, across Pont Royal, past Les Invalides and the Ecole Miliitaire, past La Sorbonne and past the Père Lachaise cemetery It's great way of seeing the city and if you get a pass, you can jump on and off. As you can see, you can also get to a lot of the touristy places on that bus.
Some other really great places in my opinion is are for example Mariage Frères which is a salon de thé (rue du Bourg-Tibourgand) is probably the finest tea shop anywhere in the world (I had an argument with my brother about this he maintained it was Claridge's, so when I went there I asked them, 'Where do you get your tea if it's not a secret?' and they said, 'We get it from a little place in Paris called Mariage Frères.)
The old plantation salon is really special
Maison de Thé Restaurant, à Paris depuis 1854 - La plus large carte de thé au monde : Darjeeling de printemps, thé blanc d'Écosse, Grands Crus de thé vert japonais, thé bleu oolong de Nouvelle-Zélande, thé noir de Ceylan, thé jaune de Chine, rooibos sans théine, infusions de fruit et Maté.
www.mariagefreres.com
Àlso Angelina (Rue de Rivoli) if you like hot chocolate. Usually really busy but probably not so many Japanese and Chinese tourists at the moment.
Salon de thé parisien mythique de 1903, proposant des pâtisseries raffinées, une carte salée du chocolat chaud à l'ancienne dans un cadre de style Belle Époque. ☕
www.angelina-paris.fr
You are a tourist in a foreign city so therefore you will stand out like a sore thumb and be a target for pickpockets etc. Paris isn't a dangerous city but all strange cities are more dangerous for tourists so beware in very touristic locations particularly train stations and airports and try to blend in as much as possible as that's your best protection (baseball cap with shorts or mouse ears for example are a bit of a give away).
Chatelet is a huge station and can be a bit rough. Also Rue St Denis at night is the red light district.
More advice: the Champs Elysees isn't particularly interesting.You will want to walk along it probably but it really isn't that interesting.
Don't eat on the Champs Elysees as you will get terrible service and terrible food. Just go off the tourist track 100 yards and everything will be much better and cheaper.
Generally, you have to be really unlucky to eat badly in France but keep out of the restaurant chains and always choose a place that looks busy and ideally has locals in it.
Try to speak a bit of French and don't criticise France if you want good service.
Restaurants and Café include service charge so you only have to leave a small tip to be polite. If you leave 20ctms for a coffee and €1 for a tip in a restaurant that's enough.
Coffee shops are everywhere including Starbucks. The coffee is ok. I wouldn't say it's great in Paris (compared to Italy) but it isn't bad.
I would advise you to wander round the Quatier Latin for food. It's a nice place anyway. But again, keep off the main tourist drags just a bit and you'll eat much better.
Rue Mouffetard is famous for the food and has a street market.
Also Rue Montorgueil has a good street market. (I love Saint-Germain en laye by the way to whoever said that and I have lived there. I think the Sunday market is a really worth seeing)
One of the cheapest and best ways to get money is simply using your credit card to buy and using your credit card in an ATM machine.
And the water is perfectly safe to drink everywhere. Restaurants have to serve you tap water by law if you ask for it. It is biologically sound pretty much everywhere in France so I have complete confidence you won't get sick. It isn't as fantastic as that superb water you get in New York but you can drink it.
You mention the Moulin Rouge- never been in but it's the red light district along from Pigale so is a nighmare to get anywhere there by Taxi as it's completely packed. I've never felt unsafe walking along there to nightclubs (they have jazz clubs although New Morning is the place for Jazz) but you will be really hassled.
Galleries Lafayette and Printemps can be got to by the RER (Auber) or Opera on the Metro. They are worth visiting but you will see pretty much the same items in them as at home. There are also a lot of restaurants around Opera and along the Bd d'italie
If you are interested in high fashion then it's Avenue Montaigne you want.