I'm looking for some (or one) good book(s) that teach linear algebra either purely coordinate-free or ones that present the standard bag-of-tools alongside coordinate-free alternatives or discussions. Thanks!
Stephen Roman's Advanced Linear Algebra. It's a gem.
You may also care to look at chapters 10-12 of Dummit and Foote's Abstract Algebra.
S. Winitzki, Linear Algebra via Exterior Products (free book, coordinate-free approach)