HDMI and DVI are essentially the same... it's just that HDMI has digital audio built-in to the same cable and uses a different connector.

I have my HDTV receiver hooked up direct to my TV via DVI, and audio going to the receiver direct via coax digital. I have no sync issues. My DVD player goes direct to the TV via component, digital audio to the receiver, while other S-Video and composite sources switch only through the receiver.

Just going by the "the less connections the better" rule, I'd say go direct to the TV where possible for video, and direct to the receiver where possible for audio. Of course, this works best if your devices support discrete input codes and you have a remote that can automate everything.