You know, I'd skip going up the Eiffel Tower in favour of going up the Tour Montparnasse - cheaper, less crowded and you get the best view (i.e. includes Eiffel Tower, you don't see the monstrosity that is the Tour montparnasse!)
Parks are generally not for playing in, sadly - lots of gravel and manicured lawn handkerchiefs. But you can hire little toy sailing boats and sticks to poke them with at Jardin De Luxembourg and Tuileries, and there's a nice fenced-in play area (you have to pay, right enough) at Jardin de Luxembourg as well.
Art Gallery-wise, Musee D'Orsay is my favourite. My advice for taking kids, which goes for every art gallery, is to have a plan of attack. Know exactly what you want to see (e.g. Musee D'Orsay, fifth floor, impressionists) and just focus on that. I usually do something kid-specific before, promise an ice-cream after, and have one parent enjoying the art, the other one facilitating the children's enjoyment of the art (pick a few good pictures and talk about them)!
Marais is lovely, often quieter than the main drag, and a good museum in the Musee Carnivalee gives the history of the city. Also nice eating places, especially for brunch. And when the kids get fed up of Haute Cuisine and baguettes, hit up Breakfast in America for their enormous and delicious pancakes.
Don't miss Notre Dame, it's lovely first thing, and then hop across to the Ile de la Cite for a cone of Berthillon, aka the BEST EVER ICE CREAM!
I'd avoid Pompidou Centre, it's ugly, concrete and where the jakeys hang out.
Montmatre is fun, with a good buzz around all the artists and cafes up at the top, and amazing views. It's a heck of a steep climb, but there is a little train that takes you up which is worth your time. Be aware that the area at the bottom is Pigalle, which is seedy, and there's quite a bit of hustling goes on in the streets going up to Montmartre.
Erm, sorry, I appear to got rather carried away here [embarrassed]