Depends really on what makes you go Wow! and how adventurous you want to be with a first timer.
Does your friend have all the gear and tied and tested comfy boots/shoes. I'm just asking incase you want a route which gives you the option of coming off the moor for a night rather than commit yourself to 2 or 3 days away from civilisation.
This site is good for piccies and places of interest.
Dartmoor walksI prefer the North Moors for wildness and views. You could head North from Postbridge or start at Belstone or Sourton just off the A30. There's plenty of tors to visit over 2/3 days and you should have no problem camping.
Alison mentioned Princetown, you could start there and head in almost any direction. Have a look at Jon's Dartmoor walk in the routes section for a taste of everything Dartmoor has to offer in one small area just South of Princetown.
I've been walking around Hay Tor and Hound Tor in the evenings and the bluebell display is worth a Wow just now. Wee ponies and foals everywhere too.
Along with the tors, there are old tin mines and workings, granite quarries, remnants of stunted oak woodland, ancient settlements, standing stones, circles and stone rows. Hope that site gives you some ideas, but not sure about suggesting a route without knowing a bit more about what you're after.