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"How to Think About Analysis" by Lara Alcock (2014) because the first part (half) of the book is specifically dedicated this aim, "[focusing] explicitly on skills and strategies for learning advanced pure mathematics." (from the author's intro). The remaining text demonstrates how to do this for a full first undergraduate course in real analysis.

Also, "A Book of Abstract Algebra" by Charles Pinter (available as a Dover paperback). The introductory sections to each chapter draw motivating lines from earlier definitions / theorems.

Other books that are good mentions, but even better after the above include the 2nd edition of Sheldon Axler's "Linear Algebra Done Right" (it motivates each development similar to Pinter) and "Topology" by K. Janich.

Of all, I have admired how they motivate without compromising rigor, using expository text alongside formal statements of definitions, theorems and proofs.