Cheap eats: the Bouillon chain of restaurants. Chartier is the original, but I really like Julien; amazing decor.
La Sarassine on the Ile St Louis has bargain formules at lunch. €15.50 for 3 courses. I took visitors there this weekend just gone.
Not French, but the Big Mamma group of restos is fun. La Felicità is an amazing food court with super Instagrammable loos. Pizzeria Populare is excellent and you can book (took my visitors there on Sat night).
Fancy: Le Train Bleue at Gare du Lyon.
Good places to find funky bars and restaurants: Canal Saint Martin.
Boat trip: Les Vedettes du Pont Neuf. Smaller boats and not so sardine like (avoid the actual Bateaux Mouches).
Best view of Eiffel Tower: take the overland metro line 6 from CDG Etoile (Arc de Triomphe). After Passy, it crosses the Seine and you have the most marvellous view.
Eiffel Tower: just don’t. Such a waste of money. Do the Tour Montparnasse instead. Much cheaper, easier to book, and more interactive/informative. If you absolutely have to do Eiffel, do the 2nd floor stairs. They release tickets 14 days before.
Museums: Galerie Dior is wonderful. The Jacquemart-Andre is my favourite for art and has a beautiful art-decorated cafe with a great formule for lunch. Le Petit Palais is an excellent free pit stop half way down Champs Elysees, with interesting exhibitions and decent loos, plus a nice cafe.
Versailles is lovely, but you’ll need the full day. Opt for the Palais Garnier (Opera house); it’s a gilded marvel and absolutely jaw-droppingly beautiful.