HTPC, or something similar, so you can copy/synch files to the HTPC in non-realtime, and then play them local to the TV.
Lots of manufacturers make small standalone devices which can have their own HDD, and work as a NAS.
Astone AP-360, 380, 400 or Zintech ZP-600T are a few off the top of my head ... they take a 3.5" sata HDD, have a few USB ports, have a USB-B style port for mounting as an external HDD, and can play most of the 1080p high bitrate stuff that I throw at them (bluray iso's) across a wired network. From the local HDD is a definite.
Most wireless connections are NOT stable enough, or possibly fast enough, to play 1080p from another wireless device. I used to be able to stream low bitrate 1080p content from a wired source, across a dedicated 802.11g bridge ... but as I said ... dedicated ... and those were great little A/P's .. I have trouble streaming 1080p across the same manufacturers 802.11n - 300Mb/s A/P's. Go figure.