Rosemont is a pretty nice place.
While it's not outstanding architecturally, it is a relatively quiet neighborhood.
It's also further away from a lot of activity than other neighborhoods.
If you let me know what your interests are, I can suggest some good places to visit.In Montreal, a lot of the action is centered around Saint-Laurent Blvd. or Ste-Catherine street.
Saint-Laurent is often called La Main as it is the main street splitting the city between East and West. There you find all sorts of funky little shops that sell everything from clothes with an Indian flair to stained glass supplies. Originally it's been a street of immigrants. You find remnants of the Jewish community, it crosses the Portugese neighborhood (you can still find some traditional Portugese grocery stores that sell dried fish in a basket) and host of other nations.
Ste-Catherine is more commercial. It goes from Westmount in the west to Hochelaga in the east (it's a one way street). It's got everything. The corner of St-Laurent and Ste-Catherine is the redlight district. and further east it turns into The Village, a neighborhood where most of the gay community is concentrated. The further east you go, the poorer the place.
René-Lévesque street is another very important boulevard that goes East-West. While it's mostly skyscrapers and big business, there is a place where you can loose a few hours. In the west, there is Cathédrale Marie-Reine-Du-Monde that is magnificent. Just next to it is the Queen Elisabeth hotel. If you ask the desk, they will let you know how to get to the John Lennon and Yoko Ono suite. A definite pilgrimage for any Lennon fan. There is a plaque on the wall to commemorate the bed-in that took place there. And it's just next to Place Ville-Marie, an emblematic skyscraper and Gare Centrale, the big train station. This is all easily accessible by metro.
The Olympic stadium also offers plenty of stuff to do. You can take the tram up the tower, it's just next door to the Biodôme, Botanical Gardens and Planetarium.
Then, there's the Saint-Joseph-Oratorio with it's life size manger exhibit. Notre-Dame Basilica that is a reproduction of Notre-Dame-de-Paris. And there's Chapelle Bonsecour which is very popular for it's boat themed decoration.
And there is also the Lac Aux Castors which is way up on the mountain and has a belvedere with an incredible view of the city. This one's accessible by bus.
For a lot of bus and metro info, be sure to bookmark the Société de Transport de Montréal
http://www.stm.info/enThey have a route planner.