Welcome to the Apple Community.
Some users with DVI have managed to get their TV's to work with DVI-HDMI cables. DVI carries no audio, so alternative connections need to be explored to enable audio. DVI doesn't necessarily support HDCP as well as other standards used by HDMI (which may or may not be an issue)
Analogue (component, composite etc)
There are hardware converters that will convert HDMI to various other types of output, however there are some issues with doing so that you should be aware of.
Resolution and aspect ratio
I'm not aware of any converters that will scale the output from the Apple TV, any TV or projector which is used will ideally need to be widescreen and support resolutions of 720p (Apple TV 2), 720p/1080p (Apple TV 3), although the Apple TV does have a number of 4:3 resolutions it supports, but these may not be available if the TV doesn't broadcast them.
Most types of HDMI to non HDMI connectors or converters won’t carry audio, in such cases you may also need to convert your optical output to an analogue signal using a DAC.
My son did hook up the DVI from my DVD player and I can get video, but can't get audio. Is there any way to get audio using that sort of configuration? You mention a DAC, what is that?
I do have an airplay that I use in another room. Can I somehow get audio with that if I were to put them in the same room?