Where to stay for 3 nights in Paris?

I don't know these particular hotels; my go to for short visits to Paris is Henri IV Rive Gauche in the 5th near Notre Dame. But of your options I would choose the 6th. I would not do Versailles with so little time unless it is the one thing you most want to see. It is a huge time suck and so miserably crowded. You can combine things e.g. walk from Concord one evening up through the Christmas Market to the Grand Palais and turn left and walk across Pont Alexandre to be on the bridge at the top of the hour when the Tower sparklers -- wonderful views in all directions and you can then return to the Champs Elysees and walk on up to the Arc du Triomphe or cross the bridge and walk back up the Seine to Notre Dame which is also stunning at night. You can easily just take a Seine cruise any time convenient.

We stayed in the 17th this fall (totally inconvenient for your purposes of course) and one of the 4 bakeries near our apartment had a wide selection of gluten free breads. We bought them for dinner parties that included a friend who needs this kind of food and she loved them. We have also seen gluten free things in shops. You will have to line up options though and I would do this through this group and Trip Advisor before the trip so you have some restaurants or bakeries more central in mind. Of course if you like seafood some of the great Brasseries on Blvd Montparnasse like Dome have wonderful seafood platters that are likely safe.

Gare du Nord- No - outside food kitchen, homeless ++ hangout, wear money belt and watch belongings in and around this station( speaking from experience).
If I am planning a short stay I look for convienence to what I want to see and the transportation I need to use.
Both others areas are good. March '16 stayed at apartment on La Motte Picquet; good access to transportation, walkable to Eiffel Tower/Seine.
6th another good area for metro connections, brasseries, cafes.
Christmas windows/decorations at Printemps & Galleries Lafayette worth it.
Ride the bus and you can see lots of neighborhood street decorations. Huge Christmas Market (open late)on Champs de Elysees, smaller ones by churches (Sacre-Coeur, St. Sulpice, etc) open later in December.
BTW- I'm traveling Thalys from Amsterdam to Paris in December for one night; using travel vouchers due to expire. Staying at Holiday Inn Notre Dame- Eiffel Tower view room. Stay awake till 1am the last time the Eiffel Tower sparkles for the night then the lights go off and the Eiffel Tower goes dark (again speaking from experience). I love Paris any time of the year, but this time of year is magical ( 11/15, 12/14, 11/13).
If you would like to go to Versailles do it. Follow RS suggestions and use his book for descriptions and explanations. In March there was not a special entrance for Museum pass holders. The Chateau is worth the trip. I would leave the other palaces in the gardens for nice weather. The grounds are massive. Enjoy

The 6th and the 10th arrondissements will be more gluten-free-friendly.
You'll need to Google specific pastry shops and restaurants before you go, so you can map these.
Any organic (bio) food store will have products with no gluten, and supermarkets will have a very small selection in the "bio" section - good idea to Google these, as well - Bio C'Bon, Naturalia, Bio Coop. Supermarkets: Franprix, G20, Casino, Carrefour.
You can get anywhere via Metro in about 20 minutes, so where you stay won't be a problem - I'd choose the hotel with the best amenities. The Metro is safe at night, as are the areas you mentioned.

Beth - after your trip, please report back about Gluten Free options your daughter and you find like bakeries and what she did and didn't like. My daughter recently dropped gluten and feels so much better. BUT, shes dreading our next trip to Europe because she knows if she eats gluten she'll be in pain but she knows how great the bakeries are! I'm curious to know your daughters experience.

Have a great trip!

Safe Travels.

Just in case you need this:
Paris By Mouth, Our Gluten-Free Guide to Paris: http://parisbymouth.com/our-gluten-free-guide-to-paris/

15 Best Places w/Gluten-Free Food: https://foursquare.com/top-places/paris/best-places-glutenfree-food

Gluten-Free Restaurants & Bakeries, Paris: http://www.glutenfreeblog.com/2015/02/gluten-free-paris-france/#.WC4EkDKZORs

Enjoy your trip.

@amyk - I eat gluten free and during my last visit to Paris in October I found a delicious bakery right next to the Arts et Metiers metro station in the Marais. I don't recall the name offhand, but it is right next to the steps that go down into the metro. They had delicious gluten free breads, rolls, etc. Your daughter should have no problem finding gluten free options in the cities in Europe.

Hi,

I am familiar with Hotel Albert 1er in the 10th, never stayed there but have checked it out for possible future stays. The hotel itself is good, location is ca half way between Gare du Nord and de l'Est. Basically, 3 mins walk after you exit Nord, turn left to the first traffic signal. You see it from there. Albert 1er is a Best Western or used to be. I saw it last in June of 2015 when I stayed at Nord.

There are lockers at Nord but not coin lockers (no where in France for those). You have to check in the luggage at a Left Luggage facility. the same at Est, where it is on the bottom floor.

Stayed at St Severin twice. It's in the 5th, a block from metro/rer, 5 minutes walk from Notre Dame