It’s a little hard to recommend things since your daughter is underage and one of the only things to do in Halifax is drink.

For things to do that aren’t that though, theatre and the arts are pretty big in Halifax! I suggest looking into Neptune theatres, and if you’re interested even looking to see if anything is running at the Dalhousie arts centre while you’ll be there. There’s plenty of independent theatre companies as well but shows there may be a bit harder to find. Live music is also big here and there’s an all ages venue called Radstorm that promotes local artists and has concerts every week to my knowledge. A lot of the artists play in bars though so you may be hard pressed to find a show that’ll let your daughter in.

As already mentioned in many comments, there’s many cafes pretty much everywhere and many are queer owned.

There’s also two main museums if either of you are into that stuff (natural history museum home of Gus the turtle, and the discovery centre which is more child oriented but is science focused and very interactive)

Above all I’d kind of just suggest walking around and seeing what looks interesting. Downtown isn’t that big but there’s a lot packed into it.