On my first trip to Montreal, I was staying with a few friends nearby and had a lot of time to kill while they were all in morning/afternoon classes. My first day, I wandered around the neighborhood aimlessly, looking for a place I could feel comfortable sitting at by myself (one of my ultimate phobias), have some coffee and maybe a small meal, and pretend to write down profound thoughts in my journal.
I came across Cafe Republique and it totally fit the bill - nice outdoor patio, coffee galore and plenty of cheap eats. I spent the rest of my mornings here chain smoking and drinking coffee for the duration of the trip and never once felt awkward sitting alone. Really pleasant cafe with really nice waitstaff.