Harmony 900 IR and RF (Radio Frequency) will go through walls for you.
This is what I use and on sale about 20 bucks over your budget. I bought mine used on ebay ($75)and absolutely love it because I can create custom touch screen buttons and still have the hard buttons for changing channels or volume in the dark.
The nice thing about it is once you set it up it is easy for your other family members to use by selecting the activity they want to use. I named my activities "watch DTV" "Watch a Bluray" "Use Computer" Once they select an activity the remote turns on the equipment and changes the inputs for your AVR ect... to quote Apple it just works. haha
you will have to plug the remote into your computer to program it with your activities and equipment however I have found the process to be simple. If you want to delve deeper you can and I customized the remote to control XBMC when I am using the watch computer activity.