I'd go in a slightly different direction. Instead of developing more depth in one branch of mathematics you will certainly study more of, consider exploring some branches of which you don't have any familiarity.
My strongest recommendation would by an easy abstract algebra text, such as Fraleigh's "A First Course in Abstract Algebra".
Munkres' "Topology" is wonderful. It isn't as accessible a text as the above, but the first portion, on point-set topology, is probably reasonable for self-instruction.
If you want to be super hip, work though Gauss' Disquisitiones Arithmeticae. It's a number theory text published in 1801 by arguably the greatest mathematician who ever lived.
If you're dead-set on analysis, I'd recommend Spivak's "Calculus" over Stewart's "Calculus". From what I've seen of Stewart, it isn't at all theory-oriented, focusing on the mechanics and application of calculus. Spivak is quite challenging, however, and may not be suitable for self-instruction.
If you just want to see what's out there, poke around MathWorld ( http://mathworld.wolfram.com/ ), or maybe Wikipedia's Mathematics Portal ( http://en.wikipedia.org/wiki/Portal:Mathematics ).
