Spend a half day around Brooklyn Bridge Park, Dumbo and the Brooklyn Heights Promenade - especially the latter given the area is about to go through a major upheaval as the BQE cantilevered section is due to go through some major renovations lasting 6+ years.
A half day in Brooklyn Museum, Brooklyn, Botanical Gardens, Prospect Park.
Checkout the breweries and coffee shops of Gowanus and Carroll Gardens.
Do the Made in Red Hook tour and check out some really interesting local makers. [1]
Visit one of the oldest buildings in the city [2]
Take a Brooklyn Pizza / Chocolate / Neighborhood tour [3]
[1] http://www.madeinbrooklyntours.com [2] https://wyckoffmuseum.org [3] https://www.asliceofbrooklyn.com/
I'll spare Brooklyn residents the pain of ratting out their less well-known haunts.