Hotel Du Levant in the Latin Qtr - we had a wonderful experience there last year.

Try Hotel du Cadran in the 7th. Right next door to Cafe du Marche and 45 second walk to the Rue Cler Market around the corner. Within 5 minute walking distance of the Champ de Mars. When we were last there, our hotel room had a view, albeit a very limited view but a view nonetheless, of the Eiffel Tower.

Op here- thanks for all these great suggestions!
Nothing against apartments- we're just staying in apts in south of France and DH wants hotel experience.

Hotel Familia in Latin Qtr. was great location, family friendly and American friendly

I travel to Paris regularly for work and stay in the 16th near Trocadero, spitting distance from the Eiffel Tower. I recommend the Renaissance Park Trocadero, a Marriott. Very nice. While not the most enchanting of Parisian neighborhoods, there are many nice cafes and you are close to the metro and Seine where you can take the water taxi/tour - which is ag great way to get around to many of the major sights!

OP, why aren't you interested in renting an apartment?
I am just curious because I am currently looking into renting an apartment in Paris and am wondering if there are some drawbacks that I am missing.

There are tons of apartment/hotel websites for Paris. A french friend just recommended mykeystoparis.com.

I got a recommendation from this site for Hotel des Balcons; we got a quad room (sleeps four) and it was perfect. Right near the Luxembourg Gardens (which is great for kids), and other attractions; and very good rates. Be aware that there's no air conditioning (which wasn't a problem for us, since the weather was perfect). You can check this cite for other recommendations, but we would definitely go back there.

http://www.balcons.com/

Try Hotel Abbatiel St Germain. It is close to Notre Dame, in a nice little neighborhood. Haven't stayed there in years, but I remember it being very nice. They also have some adjoining rooms.

Here is a list someone put together a few years ago of Paris hotel rooms with quad occupancy.--

http://www.tripadvisor.com/ShowTopic-g187147-i14-k1554693-List_of_Hotels_with_Family_Quad_rooms-Paris_Ile_de_France.html

I don't really think of the Eiffel tower/7th as being "close to all the sites" and personally I'd lean towards staying someplace a little more central (4th, 5th, 6th), although obviously it would depend on room availability etc.

Looking for a Paris hotel that is close to the sights (Eiffel tower) that can accommodate a family of 4 in early summer. I've been trying to find a hotel in the 7th arrondissement- but they are all booked up or ridiculously expensive (ie >$800/night for room for 2 adults and 2 young kids). Any thoughts??? No interest in renting an apartment. Thanks!