Mont Royal is worth a visit, on a good day. The views are spectacular and Smith House has a fine cafe. However, this review is principally about getting there.
You might consider taking the Metro to Peel station, then walking up Peel Street and onwards into the park via the southern entry point. Let me stop you now. This route might be suitable for an Olympic athlete in training for some leg intensive sport, but it is pure insanity for normal humans. The climb from Peel station to the Royal Chalet in Mont Royal Park, is epic to say the least.
Take an Uber to Smith House, in Remembrance Road, and start your explorations there. By all means walk down and you will see what I mean.