I'm going to throw out my recommendation...
Sony Audio Visual Receiver | 2-Channel Hi-Fi Receiver | STR-DH130 Review | Sony Store
This is a stereo receiver without HDMI connectivity. Keep the HDMI at the TV and make sure to use a Blu-ray player and other sources which maintain a set of RCA outputs. If you find a component that does NOT have RCA outputs, then you can pick up a HDMI audio de-embedder from
www.monoprice.com
This product, by the looks, gives you stereo audio amplification to a set of speakers in the room. Stereo only, which should be fine. It also has analog audio pre-outs which should be able to feed a set of amplified stereo wireless headphones just fine.
I use Sennheiser wireless headphones and for $80 or so they have performed very well for my 'the-kids-are-trying-to-sleep' needs.
The biggest headache is in the cabling of the setup needing to run 2 HDMI cables to the display and switching inputs will be a bit cumbersome. Perhaps worthy of a decent universal remote control.
I would expect with some entry level speakers, cabling, the receiver, and everything, you could do it for $300-$400 pretty easily.