I don't have links at the ready for all these places, but they are google-able:
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outdoor stuff
Ross Farm is about an hour out of Halifax
Shubenacadie Wildlife Park also about an hour (in a different direction)
Atlantic Playland is an amusement park type spot within Halifax municipality, about 30 minutes from downtown
Hatfield Farm has hay rides and stuff, they are not far from the Playland so within city limits
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Halifax waterfront is a great spot for just walking, grabbing an ice cream etc. I *think* your timing lines up with the Busker Festival, which is loads of fun but very crowded. You can also grab the ferry over to Dartmouth and back, kids love that. It's part of the city transit system, so it's cheap and a short trip, you can sit up on the top and enjoy the sunshine (if we ever get any, LOL! Actually, it's sunny today, so here's hoping). There is a city library (closed Sunday and Monday) in the Dartmouth ferry terminal with a nice kids area, you could head over, check out the library, and then head back to Halifax for an inexpensive outing.
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Dewolfe Park in Bedford (part of Halifax, probably 10 minute drive from downtown) is right on the waterfront and has a big pirate ship themed play structure for the kids.
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indoor stuff
Discovery Centre - a kids science centre
NS Museum of Natural History - new forest display just opened up, interactive for kids to play. They also have a butterfly house and various kids programming. I think they have an exhibit right now on the deep sea.
Maritime Museum of the Atlantic - lots of kids programming, I think
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The Halifax Farmers market is in two locations. Worth checking out. Not sure of the hours, actually - one location (in an old brewery, it's pretty fun to wander around) is weekends only, the newer one (beautiful new facility on the water) might be weekdays, too, I am not sure.
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Oh and you should check out Peggy's Cove some evening (during daylight) as a family (soyour Dh gets to see it too!). It is gorgeous there. Pick a clear day that isn't too windy. It's about 45 minutes from the city. And read the signs - they are not kidding about staying off the rocks by the water, it's dangerous! The lighthouse area gives a beautiful view and no worries about stray waves.
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I love where i live, can you tell? :P