Closest airports: Cluj and Sibiu.
From Brussels Zaventem you’ll find flights with Lufthansa, Austrian Airlines, TAROM
From Charleroi: WizzAir, Ryanair.
Taxi from the airport: about €100. Car rental is also available.
Driving in: remember to buy vignettes for Hungary, Austria & Romania.
In and around Alba Iulia:
Many options via Airbnb & Booking.com