Chora is entirely walkable — the peninsula is small enough that no point is more than ten minutes on foot from any other, and cars are banned from most of the old town anyway. The main pedestrian street runs the length of the promontory, and the steep lanes off it can be explored in an afternoon.
Between Gavrio (the ferry port), Batsi, and Chora, there are regular KTEL buses running throughout the day in summer. The journey from Gavrio to Chora takes about 50 minutes and costs a few euros. Timetables are posted at the bus stops and change between seasons; ask at the port when you arrive.
For anywhere off the main road — remote beaches, inland villages, the walking trailheads — a hire car or scooter is the practical option. Several agencies operate in Gavrio and Batsi; book ahead in August. Roads outside the main corridor can be steep and winding, so be comfortable with narrow mountain driving before taking a scooter far from town.
The island's network of old kalderimia (stone-paved mule paths) is arguably the best way to experience Andros. These routes connect Chora to Apikia, the Pythara waterfalls, and more remote villages, and many are now waymarked. A car gets you to the trailhead; the paths do the rest.