I'm thinking of places that have enough floor space/couches/etc that I'll be fine while I enjoy a tea and some much needed time out of the house. These aren't kid-destinations, necessarily, but are places that would fit the bill to avoid feeling stuck at home.
Coffee Culture on Brant downtown has couches and a cosy fireplace.
The library! Aldershot library is great, as is Central. Both have toys and books and puzzles for kids. Comfy couches at Central branch on New Street.
Tansley Woods community centre. There might even be some programs at the centre or at the libraries that you can enjoy.
ROCK Centre for Kids on Plains Road (drop-in or age-appropriate program). There is a ROCK centre on Cumberland too about which I have heard many good things.
Walk in the rain! If it's not a downpour or on the verge of freezing, I'll get out there with a baby-carrier and my Suse's Kinder Coat). The sights, sounds, feel, and smell of rain are wonderful for my spirit, and are good for my kids to experience too.
Ikea on Plains Road. You can shop a bit, then spend extra time in the kids section --there are enough toys set up there for playing with that she'll have a blast. My son calls Ikea "the store with the trains?" because I always go with a play-stop at the trains as an integral part of the trip. It is the only reason I've been able to shop with two kids, quite frankly.
And, if all else fails, I will always remember my friend's sage advice --give a baby a stir stick and the sleeve of a coffee cup and they will be in their glory. (This might mean a walk to the mall will be just what we need).