If the intent is to provide breadth, then many of the suggestions others have made are quite appealing, especially if it is made clear what branches of topology are being introduced and what a student should do outside of class to develop depth in any or all of the branches.
If the intent is to provide depth, there are likely several texts out there, one for each branch, with suggestions. I remember covering Munkres first course in Topology starting with chapter 2; even though we skipped over the set theory and foundations, I was intrigued enough by them to study set theory and foundations while in graduate school. Although the class did not go all the way through the book that first semester, we got exposed to quite a bit, and I developed more ofa taste for formalism from that class more than from any other that I took as an undergraduate.
If the intent is to provide both depth and breadth, I suggest part of it be run as a student seminar. A later toplogy course I took had me present Sard's theorem; if nothing else came from that course I at least know how to prepare to explain Sard'd theorem for my next opportunity.
Gerhard "And This Was Decades Ago" Paseman, 2012.08.22
