I'd go for Takayama (and Shirakawa-go is indeed beautiful if you have time).
I enjoyed Magome and Tsumago (not Tsugamo
), but was very disappointed by the "hike" between them. For the most part, the trail is made of concrete (!) and stays so close to the road you can actually hear the cars (you will also see them quite often because the trail crosses the road many times!...). Don't expect any breathtaking view either.
If you like real hiking then don't waste your time, just take a taxi and visit the two villages.