"Topology from the differential viewpoint" is a marvel of a book, and the most accessible one of Milnor's.

If you are not quite ready for it, or need some inspiration first, I recommend "Intuitive Topology" by Prasolov (https://bookstore.ams.org/mawrld-4/). It is short, has no prerequisites, and communicates the flavor of some of these ideas. (It also covers some knot theory, which is a different subject)

I came here to recommend that. And anyone interested in great mathematical writing should read the first few pages of Morse Theory. (The rest of the book is great too, but I especially love the clarity and directness of that opening section.)