I learned real analysis from Strichartz' wonderfully titled book, The Way of Analysis.  It is very wordy, but I really liked it.  I suspect that I would like it less as an instructor, simply because in preparing a lecture I don't need all the discussion, I just want to remember the main point.  But for a student, the discussion in this book can be quite beneficial, and of course as instructor, one can always keep a copy of Rudin close by.