Ted Shifrin's book Multivariable Mathematics is actually one of the best books of this type while not being very well known. Unfortunately, it's very expensive, so unless you can find it in your library, I would choose something else.
Otherwise I would just recommend Spivak's Calculus on Manifolds together with some linear algebra book. For linear algebra I would recommend either Axler's Linear Algebra Done Right or Linear Algebra by Fiedberg, Insel and Spence
I learned multivariable calculus from Paul's Online Math Notes.
If you want a physical textbook, I second Jared's recommendation of Marsden & Tromba's Vector Calculus. It has a somewhat more theoretical flavor to it than James Stewart's books.
Another standard text is Edwards & Penney, which I've used to tutor students. However, it's essentially on the same plane as Stewart.
Now for a few comments.
First of all, if you're studying for the GRE, then you might not want a textbook that emphasizes theory. First and foremost, you need to be able to solve basic problems and calculate things, so in that sense a book like Stewart's might actually be the most appropriate.
Speaking of Stewart, not everyone holds his books in such disregard. I don't love his textbooks personally, but I do understand and appreciate why they're the standard.
Finally, I'd like to take a second and exude some enthusiasm for the subject. Multivariable calculus is one of my favorite areas of math, and was crucial in helping me develop intuition for (and interest in) differential geometry. In my (admittedly limited) experience, undergraduates skipping multivariable calculus and ordinary differential equations is not too atypical. However, I would hope that all serious math students eventually go back and learn both subjects, appreciating them for their inherent beauty.
Best Answer
In the late 1960s through the mid 1970s there was a slight tendency (in the U.S.) to combine calculus and linear algebra, at least for honors level courses. Two books that I'm fairly familiar with (because I worked through parts of each while in high school) are [1] and [2] below. While looking up the amazon web pages for these two books I also came across [3], but I don't know anything about this book.
[1] Calculus of Vector Functions by Richard E. Williamson and Richard H. Crowell and Hale F. Trotter
[2] Calculus and Linear Algebra: An Integrated Approach by Mary R. Embry and Joseph F. Schell and J. Pelham Thomas
[3] Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds by Theodore Shifrin