Spivak’s Calculus is hands down an excellent book for a first course in real analysis, and I’ll die on that hill(it’s only real competition is Analysis 1 by Tao, in my opinion).

Anyone that says “it’s just a calculus book; it’s not good for introductory real analysis” is invited to go solve every problem in, for example, the chapter which defines integration, and compare the difficulty with problems in “traditional” analysis books.