You've got all the big sites listed, lots of people like wandering the shops on Water Street too.
With your kid, skip Raymond's and go to Ches's imo unless you have a sitter
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My kiddo dug the bird sanctuary out at Cape St. Mary too but that's a big drive, the plus is you get to see more of the real NFLD outside of "town" if you stop off in a few places along the way. For me the best part of Newfoundland is the small towns, lots of old buildings and beach combing on the rocky beaches is what my kids like to do best especially when they are that little.
Avoid the shore/CBS as it's become more like a suburban sprawl of St. John's but if you drive past there the western part of conception bay is pretty neat with Harbour Grace, Port au Grave and Brigus etc, about an hour drive out, definitely a slow pace of life out there.
I don't know what's on right now but a lot of the smaller towns have festivals and garden parties throughout the summer that are fun too.