This is normally referred to as something like "dual control dials", and you're right, it's a very desirable feature. Very few entry-level cameras have this, but it's common on mid-tier "prosumer" DSLRs, and universal on higher-end models.
You can find a list of models with this feature on a camera review / database site like Neocamera; try this search:
Right now (late 2012), if you're looking for below $1000, you have the option of buying a 2010 model, like the Nikon D7000, Canon 60D, or Pentax K-5. As of this writing, these are all around $800 body only. (In general it has historically been the case that you can get a slightly-older mid-tier model for about that price, and until there's a shakeup in the economies of the camera market that's likely to stay true.)
Or, you may want to look at the somewhat uniquely positioned Pentax K-30, which is a upper-entry-level camera introduced this year. It has a number of features normally reserved for higher-level cameras, including the dual controls, a 100%-view penta-mirror finder, and weather sealing. The camera market is very volatile and it's possible that other brands will follow suit in this area, but for right now it kind of stands alone.
Alternately, just squeaking under $1000, the Fujifilm X-E1 offers an very nice control system where you adjust aperture via a ring on each lens and a shutter dial on the top of the camera. If you miss your film camera, the controls may actually be most familiar even if the EVF is different from what you're used to.