Well for the tuner, your options are very limited, there aren't many NTSC tuners with DVI outputs on them.. An old Directv HD box like the Samsung TS-360, Sony HD300, Hughes HDHTL or LG3200 will do both ATSC and NTSC and output DVI if you're looking for something cheap... You'll need to ebay/craiglist/classified one of those units.
For the apple TV, you should be able to use an HDMI to DVI cable or adapter.
The Xbox can only be hooked up if it's got an HDMI out and you'll need an HDMI to DVI cable for that also.
To hook all three up without the need to keep switching connections, you'll want a DVI switcher.
This is all dependent on the display accepting HD resolutions also, make sure it can accept 720p/1080i over DVI...