Which program should I do the design in? Photoshop or Illustrator, or a combination. Depends on what the design looks like
What size should it be? 11"x14" or 8.5"x11"
Does it have to look exactly like the work of my designer? No, it can be more contemporary in look, or designed somewhat differently. But should have some major identifying characteristics of your designer.
Where do I get venue info? You can make it up
What if my designer only designed fonts? Create a poster that features his fonts in an interesting way,but can include other relevant imagery, pictures of the designer, quotes from the designer, etc.