Currently Venice of the north isn't it Lal
Anyway a lot depends on what you are interested in - personally I would give a lot of the big museums a miss since they often contain stuff similar to other major museums in the world and I generally feel (unless you have a special interest of course) that it is more important to see London and Paris than to see their collections of Egyptology for example... go and see the stuff that is unique to the country is possible... In Paris I would say go to the Louvre for the fantastic pyramids - well I love them (my dad called them "an abortion"
) and go in for the Mona Lisa if you must .
I am probably a philistine but after all the hype it is rather an anticlimax to discover that it is just very small brown painting hanging on a wall. Personally I would rather avoid it and spend the time at the Musee Rodin - the sculptures have so much impact and some are heartstoppingly lovely or at the Musee de Cluny which houses the Lady and the Unicorn tapestries. Both are small museums in historic buildings and display genuine french culture. Of the higher profile museums The Musee d'Orsay has the Impressionist collection which may not be a big draw considering how many fine collections of them are in the States but it gives a fine view of the Seine. Personally I wouldn't bother going up the Eiffel tower - the best view of Paris is from the Sacre Coeur (and you don't have to look at it from there! - don't go in unless you have a penchant for concrete interiors and religious themed tat).
Notre Dame and the Ile St Louis are great places to explore. My restaurant knowledge is more than a decade out of date alas but the Latin Quarter was usuallly the best bet....