Where are electrons located according to modern atomic theory?

I hate these kinds of questions, because the mental picture most people have of atoms is so very wrong it's hard to know where to start.

When talking about electrons in atoms, the first thing to know is that they're in orbitals, which are not at all the same thing as orbits. They're not going around and around in circles, they're... somewhere inside a sort of "cloud", and are more likely to be found in some regions of the "cloud" than in others.

There are equations that describe the probability of finding an electron in a given orbital at a particular point in space. These equations are called "wave functions," and are pretty complicated. If you really want to know, I recommend two books in particular: either Levine's Quantum Chemistry (better if you're approaching things from the chemistry side and/or want all the details at an advanced level) or Feynman's Lectures on Physics, volume III (better if you want more of an overview at a college sophomore physics level, or are more of a physicist). Both of these will be in any good college library, and may be in some public libraries with better-than-average science sections (the Feynman in particular).

Multiplying these equations in a particular way and integrating them gives you the probability density... how likely it is to find an electron to be in a particular region. The interesting thing about these probabilities is that they have nodes... regions of space where it's actually impossible to find the electron, though it could potentially be found on either side. For example, a p-type orbital has a nodal plane. The electron can be above the plane or below the plane, but (and this is the part that gives most people conniptions, the first time they run across it) it can never be found in the plane itself. Not even briefly. Not even "just passing through." So how does it get from one side to the other? It... just does. And all the math works out. But to really understand it, you've got to forget pretty much everything you think you know about how the universe works, and learn to trust the math.