Kenilworth Castle is worth a visit, imo better than Warwick. The back to backs don't take very long so suggest you plan something else in Brum that day. The museum is brilliant.
I can recommend Black Country Museum, we last went in 2014 and it is still as good as it was.
If you can get in a concert at Symphony Hall it is truly wonderful and I don't feel the least intimidated by the canal at night. Old perhaps but they are not in any way threatening. Just don't walk up Broad St on a Friday or Saturday night!
The Botanical Gardens in Edgbaston are good and if you want to treat yourself to a special meal Simpsons in Edgbaston is good. Apparently Brum has more Michelin starred restaurants than anywhere else outside London.
Hope you have a great time.
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