I'm not sure whether the following is too advanced, but I found
"Introduction to Topological Manifolds (Graduate Texts in Mathematics) (Paperback) by John Lee"
quite readable.
(Edit: As Ho Chung Siu pointed out, Lee's Intorduction to Topological Manifolds is written in a different spirit to Do Carmo. I'm sorry, I totally misread that the questioner is searching a kind of "Do Carmo text" (so elementary texts in curves and surfaces are searched, right?). Perhaps Lee's Introduction to Smooth Manifolds is more appropriate, but I think it's also too advanced, but anyway my suggestions below should be adequate.)

If this is too advanced for your purpose, I would recommend
"Elementary Differential Geometry by Christian Bär (see for exmaple here)"

Furthermore I would warmly recommend Nigel Hitchin's lecture notes "Geometry of surfaces" : http://people.maths.ox.ac.uk/~hitchin/hitchinnotes/hitchinnotes.html

I'm not sure whether the following is too advanced, but I found
"Introduction to Topological Manifolds (Graduate Texts in Mathematics) (Paperback) by John Lee"
quite readable.

If this is too advanced for your purpose, I would recommend
"Elementary Differential Geometry by Christian Bär (see for exmaple here)"

Furthermore I would warmly recommend Nigel Hitchin's lecture notes "Geometry of surfaces" : http://people.maths.ox.ac.uk/~hitchin/hitchinnotes/hitchinnotes.html