[NOTE: I don't condone starting in C++ as a first language anymore.]
After further investigation and actual use, I would like to now recommend Michael Dawson's book "Beginning C++ Game Programming". I went to the book store, rifled through a ton of C++ programming books and after getting through my filter I settled on this book for my son Michael to start with.
Even though the title of the book sounds like you'll be getting into a bunch of fun game stuff the reality is that all the focus for the first 8 or so chapters is just on learning C. C++ comes in during the next couple chapters and builds upon what you learned about C but doesn't go too far - it keeps it simple.
Along the way you use the language to construct a few simple games that are all text-based which I believe is a great way to just focus on learning the language and some basics about game construction. So don't be expecting to be drawing graphics and making sounds and using the mouse on a graphical screen - you need another book to do that and it should be AFTER you get through this one.
I got Michael a book on coding game graphics that he's diving into now since he finished this book. I'm proud to say that he can program in C++ now after finishing this book and it's not an overly long one either. It's also very easy to understand with good explanations for the concepts.
Some things I would have liked to have seen in the book were explanations of switch() before its use, using struct{} and explanations of complex data structures, and explanations and use of printf. The book relies heavily on cout and cin which I'm not too fond of because of the syntax but they're easy to understand when it comes to printing string objects. When Michael was going through the book I taught him printf and had him convert all the couts in the book to printfs - it showed him more about what goes on inside those string objects and was less typing when he needed to print %d, %s, etc. arguments.
One important note: the gaming college Full Sail uses this book as their introductory programming course book. Michael went into Full Sail right after finishing this book so he got to do it all over again. Much easier the second time!
Try it.