We've been going to Montreal for about 8 years and have a small apartment overlooking the Old Port of Montreal. It is one of our favorite cities in the world for many reasons. We stayed at a number of different places when we first were going up to Montreal before getting the apartment and we still have friends and family stay nearby when they visit.
All these recommendations are either on Rue St Paul or within one block.
Les Passants du San Soucu This is a charming little 9-room inn/B&B in the heart of Old Montreal near the Place Royale. The inn is in a restored 18th century warehouse with beautiful wood floors and stone and/or brick walls. Jerry and I stayed here once and loved laying in the bed listening to the jingle of carriage bells below on the streets. The full breakfast was excellent. Two heads up. It is VERY popular and is often booked...so plan ahead. And it also doesn't have an elevator imporant for those who have difficulty with stairs.
Auberge Bonaparte. This was my mother's favorite place to stay when she came to MOntreal. The 30-room inn is housed in an 1886 stone building with large wood floored rooms, attentive staff, and a very nice breakfast included which is served in the restaurant on the first floor. Before we had an apartment in Montreal we stayed here several times and always had a very pleasant stay. My mother liked the rooms on the "back" side because they have a view of the private gardens of the Basilica de Notre Dame.
Mariott's Springhill Suites is probably among the most budget friendly hotel within Old Montreal.The rooms are large and most are "mini-suites". My brother in law often stays there...the mini-suites are nice if you need a bit more room. It's on a very quiet side street
If you'd like to splurge....we'd recommend the Hotel Nelligan which is in a series of beautifully renovated warehouses into. It has it is both warm and homey and yet elegant. We stayed there when it first opened years ago. There is a nice bar and breakfast.
Another hotel we've heard good things about is the Auberge Vieux Port (I think its owned by same group that owns Hotel Nelligan). It faces directly onto the Old Port.
There is a new boutique hotel called Le Petit Hotel on Rue St Paul...but we haven't stayed there. It is in a good location but that's all I know. http://petithotelmontreal.com/
There are of course hotels like the Westin and the Intercontinental (and I think the new Hyatt is open now) that are close by but are on the "edge" of Old Montreal and tend to cater to the business crowd (they are all near the Montreal Convention Center.
Enjoy Montreal wherever you stay...it isn't difficult.