Okay here my suggestions (my previous answers were written on my iphone or ipad so not conductive for a lot of explanations/suggestions).
Transportation:
From the airport, the taxi fare for downtown is a fixed rate (approx. 35$). Theres an express bus too but at 8$ per person I would take the taxi for a family. If you leave the airport during rush hour you might be stuck in traffic. Even more true if its snowing. But since its a fixed rate, its not more expensive. The rest of the time, I would walk and take the metro/bus system. You can buy a day, weekend or weekly pass. Heres the link to the STM (city bus and metro):
http://www.stm.info/en You can also easily walk all over downtown, either outside or in the underground city (mostly for shopping). The city is really safe and unlike many American cities, Montreal downtown area (and surrounding areas) is very safe and alive on evening. Its were most people go out, where the good restaurants and clubs are. Even in the more shady streets/areas I would walk, especially if Im not alone.
Lodging:
I cannot recommend you a specific hotel as I never stayed in a hotel in Mtl before but check websites like Trip Advisor and you can always ask me if the area is nice once you have some candidates. I would personally stay between St-Denis and Guy streets (extended downtown) south of the mountain (Mt-Royal). In that area you have everything: small inns, value chains like Choice hotels, moderates and deluxe hotels (including Ritz Carlton, Loews Vogue, Queen Elizabeth II, etc.). Try to be close to a metro station if you dont rent a car.
Dining:
You will find restaurants from around the world here. From a libanese fast food (yum!) to the high end steak house (Queue de Cheval). Most restaurants are authentic. I work downtown (west) and my favourites are Étoile des Indes (Ste-Catherine/St-Mathieu) for indian, Juliette et Chocolat (for chocolate goodies and crêpes) and Wieinstein and Gavino (Crescent) for fun atmosphere but loud. The main streets for restaurants are St-Denis, St-Laurent (north of Sherbrooke), Ste-Catherine, Crescent and most of old Mtl and old port. For local cuisine you have the fast food specialties and high end restaurants that need to be reserved weeks in advance like Pieds de Cochon or Toque!. On the fast food front you have to try poutine but beware that its not good everywhere. NEVER eat poutine at McDonalds, Harveys and co. The best poutine IMO is in QC city but in Montreal I like the poutine from La Belle Province (multiple locations) and Valentine (you can find one in the Cours Mont-Royal food court). A good poutine needs cheese curds (not grated cheese or cubes), thick and oily fries and good gravy. Simple but hard to find the right combination. I usually take my poutine with a side of mustard/coleslaw hot dog. You also have to try what were renowned for, smoked meat and cheesecake. You can usually find both at the same delis. Finally, dont leave Montreal without eating a proper bagel from St-Viateur bagel shop! Since you will visit during the holidays, it might be difficult to find restaurants open after 5pm on Dec 24th, on Dec 25th and on January 1st. I know some friends who in the past would go out on Dec 25 to eat in Chinatown and then go for a movie (some of the only places open that day). There are a few grocery stores in the downtown area so you could make some purchases before they close for Christmas.
Activities:
Theres lot to do in Mtl. Many museums, parks and activities. During the holidays the first thing that comes to my mind is the ballet show The Nutcracker at Place-des-Arts. I also LOVE the biodôme and the planetarium is just next door. You absolutely have to go for a walk on Mont-Royal and if theres enough snow the sliding and skating might be in operation (you can rent everything you need). If you want to attend a Christmas mess or service theres many churches (mostly catholic and Anglican) in the downtown area. If you want to meet Santa, the real one (the one from the parade) is close to the food court of Complexe Desjardins. Hes so popular that you need to get the equivalent to a FP- to meet him. You can also meet him in the other malls but theyre not as nice/real. And like I suggested above, if you can go to Qc city during that time of year, do it! Theres a bus leaving every hour (takes about 2h30) or you can buy tickets on the Via Rail train (takes about 3h).
Weather:
Usually December is not a very cold month. Yes its cold if you compare to Florida but we have much colder at the end of January, early February. The temperature will rarely go below -10C (14F) and we often had mild early January with rain (yuck). For snow, we had big snowstorms during the last two holiday seasons but its not a guarantee. In fact, Montreal had some grey Christmas in the past. Rare but possible (unlike Qc city that ALWAYS have a white Christmas). If a snowstorm hits the city the sidewalk are a little difficult to navigate in the first 24-36h but downtown is a priority for the city so snow is removed quickly. If you dont already own a snow jacket, I wouldnt buy one to visit unless you plan on going skiing. You can survive with a fleece jacket over a windbreaker. The trick will be to have a scarf, gloves or mittens and a warm hat like a tuque. A nice store to buy all those winter accessories is Simons on Ste-Catherine. Boots are a plus but not mandatory either. Just if you wear trekking shoes/boots with wool socks you will be fine (no cotton socks in winter or you will freeze). Also, if you plan on walking a lot, long johns (leggings under pants for women) are a must!
French:
Montreal is mostly a bilingual city (not officially). Quebec is not. The province ONLY official language is French but you can get most services in both languages, especially in touristic areas. Its possible that some people working the metro booths, bus drivers or other service workers dont understand everything in English and dont speak the language. But usually if you stay downtown that shouldnt much of an issue. In fact, if you try to speak French most will switch to English even if their English is worse than your French. Dont be offended please, they just want to be friendly and its kind of an automatism. The rule in Mtl is that east of St-Laurent street is mostly French and west is mostly English.
Bon séjour chez nous!
