There are plenty of things to do in Paris with kids. You could visit the many parks that dot the city like the Parc des Buttes Chaumont where kids will have a grand time. You could also plan a picnic in the parks along the Seine. In summer, Paris Plages transforms the Seine riverbanks into temporary beaches with lots of activities for kids. Centre Pompidou also has a kids section. You could get your kids interested in Paris attractions with the Tootbus Kids Guided Tour.
This list is obviously long for the City of Love. Our top recommendations would be a romantic dinner cruise on the Seine, a stroll along the banks of the Seine or Canal St Martin hand-in-hand visiting cafes, watching the open-air cinema with a picnic at La Villette park, visiting the Love Wall at Montmartre, and of course posing in front of the Eiffel Tower and waiting for it to light up.
If you wish to spend your day exploring just museums, get the Paris Museum Pass. You could do a full loop with the Louvre, Musée d'Orsay, and Musée Rodin. You could also throw in a few other galleries and historical monuments en route like the Picasso Museum, 59 Rivoli, Musée National d'Art Moderne, and Conciergerie.
Of course, you can. Take any of the Paris airport transfer services to the city and club it with a hop-on hop-off pass. Take a full loop on the hop-on hop-off bus which might last about 2 and a half hours to get a grand overview of the city. If time permits, you could even get down at one of the most iconic sights like the Eiffel Tower, and explore a bit.
Frankly speaking, Paris is not cheap. A day's exploration in Paris can typically range from €100 to €300. These costs change significantly based on individual choices and lifestyle preferences. But you can up your money-saving game, with transit passes, hop-on hop-off Paris tours, and TurboPass.