After getting the SecretPotion from Cynthia, head to Route 210 and cure the psyducks of their headache. Route 210 leads to Celestic Town. You will ideally need to use Defog (obtained from inside the safari game) to get through this route (you can get through without it but with great difficulty and Celestic town will also be covered in fog).
Once you get there, go to the Pokemon centre and speak to the gentleman next to the stairs, he will give you a Great ball. There is no Pokemart but various items can be purchased from the house in the Northwest corner of town.
Go to the centre of town where the Galactic grunt is blocking the entrance to the ruins and battle him. He will flee when defeated and the town elder (Cynthia's Grandmother) will come and thank you. She will prompt you to give her the Old Charm given to you by Cynthia and then encourage you to explore the ruins. Enter the ruins and engage with the picture on the back wall. The town elder will come and tell you about the ancient pokemon and give you the HM03 Surf. Leave the ruins and you will be met immediately by Galactic Leader Cyrus. He will only speak to you and move on.
Route 211 and the entrance to Mt Coronet is to the West of the town. Enter the cave and walk south. where you will find an escape rope. You cannot get any further through this route without Strength, but it is worth exploring the long grass near the cave entrance as there are higher level wild pokemon here, including Machoke, Noctowl, Meditite, Zubat and Graveler, all at about LV 26-28.
You can now return to Hearthome city to challenge Fantina (so you can use surf outside of battle).