Need Advice for AV Receiver

I will start this out by saying I'm a total novice when it comes to electronics, so any any advice that can be given will be greatly appreciated.

I just finished my basement and from a closet have run HDMI lines to my theater area and bar area where each will have a 50 inch Sony LCD. The theater area is wired for a 5 speaker system and the bar area will have 2 ceiling speakers. I am planning getting 2 HD Direct TV boxes for the closet, so that I can watch 2 different games at one time. I will also have a Blue Ray Player and an Xbox in the closet.

Will a 7.2 receiver with two HDMI outputs give me the ability to watch both games at the same time with different audio in each area? and if so what is good receiver that won't break the bank?

Also, will I be able to have both TV's on different games with no sound but have music playing through all seven speakers?

Lastly, I need an RF remote to everything, I have been looking at the Harmony 900 and 1100 are these good? or is there something better?

So what you are saying is there is no way to get HD to both TVs through the receiver if I want two different games on at the same time? I'm assuming I'm going to have to run HDMI cable directly from one of the Direct TV boxes to one of the TVs and by pass the receiver to accomplish this?

$1000-$2000