I've heard from a number of readers lately asking for suggestions for visiting Paris with kids. And while I'm happy to do my best to answer your specific questions individually, I thought it best to devote a post to some of those that are more generic.
The number one question everyone has, "what should we do?" is unfortunately one that's nearly impossible to answer. The very French answer, "it depends" applies here because kids differ so much in their interests. Some kids will want to climb the towers at Notre Dame. Others will pronounce it boring. While travel is a great way to expand kids' horizons, you will be most successful if you pick sights and activities that build on existing interests.
Hotels: I haven't stayed in a hotel in Paris since 1987 so I don't have any specific suggestions to share. Frankly, though, if you're staying for more than 3 days, your best bet is to stay in an apartment where you will get more room per euro (for example, separate living and sleeping areas so you don't have to go to bed when your kids do) plus a kitchen for making coffee in the morning, keeping snacks refrigerated, and even making a simple meal (or something from Picard!) if you can't handle another dinner out. We've had good luck in other cities with www.vrbo.com but there are lots of agencies that rent apartments too. You won't get daily maid service or a concierge to give you recommendations and sometimes the decor is a little funky, but to me, the advantages are many. And what's going to make you feel more Parisian than running out to the boulangerie in the morning and bringing back fresh croissants?
Restaurants: We don't eat out a lot as a family here, much less than we did in DC because restaurants are expensive. (See sticker shock below.) But when you're on a vacation, you are going to eat out. There are chain type restaurants here that are family friendly in the American sense (Bistrot Romain, Chez Clement, Hippopotamus) but you don't have to go to these places to find something the kids will eat. Most casual cafes and brasseries will offer poulet roti (roasted chicken), saucisson (sausage), croque monsieurs(a good bet for those who live on grilled cheese), or omelets with a heap of fries. Plus all such restaurants post their menus outside so you can take a look before making a commitment.
You can certainly get hamburgers here but they don't taste like American ones and be aware that they come pretty bloody. Pizzas are served as individual portions but most places don't mind if kids share. A creperie is also a good bet for kids, although your kids might get freaked out if there's a runny egg on top. Just say, "sans oeuf, s'il vous plait" and generally they will oblige. I don't think that high chairs are widely available but then again, since my kids are way past high chair age, I may be wrong.
Get the kids involved in the planning: Dragging your kids from must see to must see is a recipe for disaster. Far better to skip the Louvre if they really aren't into art and instead go to Musee des Arts and Metiers where there are tons of cool vehicles and machines from days gone by. Your kids will feel empowered if they make some of the choices and a kid who's feeling a bit in control tends to be a happy kid. My kids, for example, like to be navigators on the subway. My favorite guide book is Open Road's Paris with Kids by Valerie Gwinner because it has all kinds of creative suggestions to spark kids' imaginations.
Go at a kid pace: A vacation that is a relentless succession of museums and churches is a downer for everyone. Remember that your kids need time to play on vacation just like at home. Take a picnic to the Champs de Mars and let them run around while you sit on a bench. Stop at a playground in a pocket park for a half hour in the sandbox and slides. Rent a toy boat in the Luxembourg Gardens. Get an ice cream to lick while you wander a quaint neighborhood. Count Smart cars or Velibs.
Be prepared for sticker shock: Unless you live in New York, London, or Tokyo, you're going to find Paris expensive. You can save money by picnicking at lunch (you can pick up lunch fixings at a boulangerie or grocery store) or by eating your main meal of the day at lunch (which tends to be cheaper than dinner) and then having your picnic for dinner. Buy your metro tickets in a carnet (booklet) of 10 rather than one at a time. Having a coffee in a cafe may set you back 4 euros but strolling the banks of the Seine or sitting on a park bench in the Tuileries costs nothing. Skip the elevator that goes to the top of the Eiffel Tower and instead buy the cheaper ticket that lets you walk up to the second level; trust me, that's plenty high enough. Many museums are free for under 18s and museums run by the city of Paris are free for everyone.
Strollers: Paris has not quite made the leap into handicapped accessibility so if you're pushing a stroller, beware. There are steps everywhere, especially in the metro. Parisians are very big on front packs and back packs to tote their babies for this reason.
And finally something that's not Paris-centric but nonetheless important....
Make them carry their own stuff: Why is that the mom always has to carry everything? I got my kids small bags with a cross shoulder strap and now when we travel, they carry their own bottle of water, a small snack, sunglasses or a hat, and all the brochures and maps they pick up along the way. This doesn't work for the little ones but anyone over 5 is old enough to do this. I also think anyone old enough to tell time should wear his or her own watch, if nothing else to avoid the continual requests of "what time is it?"
Enjoy your trip!