You'll be launching forth from the city of Sighetu Maramatiei in the North and assuming Vlad doesn't Impale the shit out of you, staggering heroically a week later over the finish line in Hunedoara.
They're both easy to reach from the airport of Cluj Napoca so getting in and running away is easy.
The best option is probably to fly into Cluj Napoca. From here you can:
Get a train to Sighetu Marmatiei (roughly 7 hours, a couple of times a day)
OR Get a bus to Sighetu (roughly 5 - 6 hours, 2 buses per day) These often include a stop in Baia Mare.
Taxis would take around 3.5 hours
You can also fly into Bucharest and get an overnight train.
Hunedoara - Cluj: Buses take approx 3 - 4 hrs.
Train: No direct, taxi to Simeria then 5 hrs
We've heard Rome2Rio is a good website to look at transport
As is this one: https://www.virail.com/
This website is for coach travel: www.autogari.ro/Transport