I am bound to recommend my book
Topology and Groupoids, (2006) Ronald Brown,
available from amazon.com . An e-version is also available from www.kagi.com for £5.
See my web page http://www.bangor.ac.uk/r.brown/topgpds.html for links to reviews.
It takes a geometric approach, and at the same time a categorical view, that is, there is an emphasis on constructing continuous functions. The approach to the fundamental group via groupoids goes a long way beyond a first course, but then the results go beyond other books, for example on the fundamental group(oid) of an orbit spaces, and a gluing theorem on homotopy equivalences.