You should know that the airport is nowhere near old Montreal and downtown. It isn't really near anything besides airport business hotels.
You will need to either take a taxi to downtown which is a flat rate (~40$). Or take the 747 bus to and from the airport to downtown. It is 10$ and includes a transit pass (bus and metro) for the rest of the day. This is very practical as you will want to take the metro downtown and to Old Montreal.
You should definitely check out old Montreal and walk around, see the old port and Notre dame basilica. Also Downtown and the underground city. If you have time maybe even Mount Royal and saint Joseph's oratory.Edited: 25 February 2018, 15:32
If you stay downtown it might make more sense to see more. Depends on the time of your departing flight.
Saint Denis street (shopping) is not what it used to be. There are some good shops but I think your time would be better spent in the underground city. (Linked underground malls and tunnels below downtown) just some of the malls include, Eaton Centre, Place Montreal Trust, Place Ville Marie (PVM), Promenades cathedral, les cours mont royal, just to name a few.
I think time is better spent there and in Old Montreal. Given the amount of time available.
LeeJaye1, I love the idea of a Mount Royal sunset - thanks for that suggestion! I think we'll stay out of the malls in order to really soak up some cultural ambience, but Notre Dame is definitely on the list, Email1010 :) Our flight is at 7:30, so I'd feel more comfortable staying within a few minutes of the airport - we'll still have a good 8 hours or so to go on an adventure, though! Unless there is a must-stay hotel, in which case it would be worth it...Edited: 25 February 2018, 21:47
Your plan is a good one; afternoon and evening in Old Montreal....and you can easily walk north for 10 minutes or so up McGill or St Laurent to downtown core...or to St Denis mentioned that is about 6 blocks east of St Laurent.. Depending when in July, you could run into Jazzfest or comedy fest which both have extensive free outdoor shows. I wouldn't bother personally with Mount Royal as it is a bit far away and would require metro and bus ride to get there.
Aloft and Sheraton are closest to terminal (except for Mariot that is in terminal) but any you should be safe with any hotel that offers a free shuttle.
Good point about Jazzfest, Capfan! Yes, I think it's all about the walking, too. Mount Royal sounds quite cool, but I don't think we want to stress about getting there (unless my daughter WANTS to check out the metro, which might be a neat thing in itself for her). We'll play it by ear, but heading to Old Montreal first before wandering is a good 'plan'. Thanks!
Metro is really easy to navigate and will save you walking. Also broadens the choice of restaurants. 3.25$ each connections included for 3 hours. Or weekend, evening, 3 day unlimited passes are also available.
It's highly recommended, and it's one of the quietest in the world (rubber tires), modeled after the one in Paris.
It's fast and convenient for old Montreal and downtown.