For a whistlestop tour (could/have spent weeks on the moor, let alone just a quick drive by - treat the journey through as a recce for a later revisit, maybe), I would head down the A38 to the Drum Bridges roundabout, signposted to Newton Abbot and Bovey Tracey, heading North towards Bovey Tracey up the A382. Turn left (West) onto the B3387 towards Haytor Vale and Widecombe-in-the-Moor (of Uncle Tom Cobley fame - great ice creams in a little shop whose name escapes me... but IIRC it's on the right as you go round a right hander downhill after the church in the village) At some point, the road changes number to the B3357 but it's the same road, signed to Dartmeet, Two Bridges and Princetown (among others IIRC). At (or just after) Two Bridges, bear right, staying on the B3357 (unless you feel the need to visit Princetown for Dartmoor Prison!!!) for Merrivale and Tavistock. That's pretty much the end of Dartmoor, but carry on down the A390 and you'll arrive at Callington, where you can head up the A388 to Launceston and North Cornwall or down the A388 to Saltash for South East Cornwall or carry on down the A390 to Liskeard and Bodmin for West Cornwall.
Other routes are obviously available but the one above will give you a quick overview of what Dartmoor has to offer in the way of Tors, rivers, wide open landscapes, pretty little villages, market towns and narrow lanes!
Hope you enjoy whichever route you take as well as the real holiday in Cornwall.