The Botanical Gardens are lovely, Ile Notre Dame (metro Jean Drapeau) has some pleasant gardens and the Biosphere (not the Biodome) there is one of my favourite Montreal museums. Walking up the mountain is an enjoyable activity. If you like to cycle, biking out to Lachine is an enjoyable activity on paths all the way from Old Montreal. Getting to the Lachine Rapids is one of my favourite cycling excursions, although the route there is a bit convoluted, not a straight shot like to Old Lachine.

Plateau Mont-Royal, Jean-Talon Market, Atwater Market interest areas to go shopping... not at all like downtown. Lots of great restaurants in the city... I tend not to go for bistros so much (I do like cozy but the word "bistro" doesn't fit what I usually go to: home-cooking, healthy, vegetarian, flavourful, local, reasonably-priced (I like cuisines of many different nationalities) would describe my haunts), so can't advise particularly. On a rare occasion I went to a bistro; I thought Chez Victoire on Mont-Royal Avenue in the Plateau was pleasant.

Even though you've been before, with 3 days only, I don't see any need for a day trip out somewhere. Plenty to do right in the city. (I'm not big on Tremblant personally...too artificial. I have favourite day trips; some Montrealers will probably be surprised to learn that Trois Rivieres is one of them!)

There is so much to see and do in Montreal, you could easily fill 3 days. Dan had some good suggestions. If you haven't experienced the plateau area, you haven't experience the 'essence' of Montreal (IMHO). This very French neighborhood is filled with small, interesting places to eat (many byob), funky little shops, parks, and quiet tree lined streets. The liveliest part of the plateau centers around St. Denis from Sherbrooke up to Mt. Royal.
Other things to explore might be the living history museum and grounds of Maison Saint-Gabriel, the pleasant less touristed neighborhoods up on the north end of the city, like Rue Fleury, and the mile end.
If you visit the last week in June, you will be there for the Jazz Fest - one of the largest music festivals in the world - much of it is outdoors and free.

I really like the Pointe-à-Callière museum of archeology in the old port area.
Even though you have seen the Fine Arts museum already, think about the special exhibit of the Chinese terracotta warriors, there through the end of June

I agree with others you should explore the Plateau area.

In the Eastern townships I recommend the abbey of Saint-Benoit-du-lac and the wine route. Chambly is also an interesting side trip. But you could find plenty to do for 3 days in Montreal

There are many spots to visit in Montreal but the choice of spots basically depends upon the individual interests. Personally I enjoy a lot wandering around the old city, Montreal Botanical Garden, museums and many other attractions. If you are an architect lover then also there are many good options like Olympic Stadium, Saint Joseph's Oratory of Mont Royal, Notre-Dame Basilica.

Thanks for your suggestions. I've read about the Botanical Gardens but not yet visited and that is a good idea. I have visited the abbey of Saint-Benoit in past, but any similar day-trip ideas would be welcome. The markets are also a good thought although I'll be visiting on weekdays and will have to research when and if they're open. And yes thanks for the tip, I forgot that the Jazz Fest is on at that time of year.

The Jean Talon and Atwater markets are open on weekdays

The tourism web site for Montreal is very good, with information about the different neighborhoods (look under the Discover tab) and attractions and a calendar of events.
http://www.tourisme-montreal.org/