With a budget of $2000 you are more than adequately geared to get yourself a very nice unit that will do whatever you want and more.
Basically speaking, you need a unit that will power a remote or zone 2 location and perhaps some HDMI pass through would be nice, too.
I recommend either the Onkyo TX SR805 or TX SR875 (which are both under your budget, the 805 is well below) because it's only what I am familiar with... that being said other receivers will do the exact same (more or less) as the onkyo.
As I said above, with a budget of $2K you can afford a very nice piece of equipment, so pretty much any decent modern receiver would fulfill your quite undemanding requirements for it.
Good luck.