At the bottom of Cycling Road, you'll reach Route 207. Head east. You'll encounter Dawn/Lucas, who will give you the Dowsing Machine Pokétch app, useful for finding hidden items. Continue east to the entrance of Mt. Coronet.
Mt. Coronet is a significant landmark in Sinnoh. For now, you'll only traverse a small section. Inside, you'll meet Cyrus, the enigmatic leader of Team Galactic, for the first time. He'll give a cryptic speech and then leave. Continue through the cave, battling wild Pokémon like Zubat and Machop. You'll emerge on Route 208.