The DVR (you called it a DVD has HDMI output so the classic setup is...
All sources to the Sony Your DVR has HDMI as well as your TV and DVD.
So the best setup is ...
DVR -> Sony -> HDTV all with HDMI.
If you have an antenna that goes to both DVR and HDTV.
Final connection would be an audio optical cable from HDTV back to the Sony.
There is no need for coax here.

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