Nacrene City

Enter Nacrene City and go through the gap in the north fence to find a hidden Ultra Ball in Pinwheel Forest.

Return to Nacrene City and head east to the Pokemon Center to heal your Pokemon and restock items.

Go west from the Pokemon Center and enter the first house. Talk to the bald man, the final Move Tutor, who teaches moves in exchange for Green Shards.

On the west side of the house's bottom floor, a man runs a battle shop selling various Battle Items.

Leave the house and continue west along the old railway tracks until you reach a white fence. Use the Dowsing MCHN to find a hidden PP Up.

Return east to the Pokemon Center, then move north along its left side.

Head west to the cafe and enter. Go down the steps to the lower level and talk to the woman.

Answer 'Yes' to her question to receive a Dirty Handkerchief.

Head east to the Museum and enter.

Talk to the Scientist inside, who introduces Lenora.

Lenora will offer you a fossil. Choose the first option for a Cover Fossil (to regenerate Tirtouga) or the second option for a Plume Fossil (to regenerate Archen).

Confirm your choice to receive the fossil.

Lenora's husband will give you a tour. You can explore the old gym upstairs, but there is nothing there.

Return to the entrance of the museum and talk to the woman at the right counter.

Deposit a Pokemon at the PC in the Pokemon Center to make space in your party, then return to the woman to have your fossil regenerated into a Level 25 Pokemon.

Exit the museum. If you don't want the regenerated Pokemon, you can swap it with the one you deposited in the PC.

Head through the eastern gate to Route 3.