Fable/Mayor's Invitation

After the arena you will hear that the mayor has some interest in you. Go to Bowerstone talk to her and the woman beside the jail. You will then have to buy a black rose and give it to her as a gift. This can be bought just in the shop by your current location. She will then ask you to find her necklace. Walk around the current area and speak to all the men, one of them will tell you it is in Oakvale. Talk to her once more and she will tell you to retrieve it.

Go to the Oakvale graveyard; two thieves will be whispering about the theft. Sneak up the hill behind them and they will reveal that it is hidden between the two boats on the beach. Dig in that spot and you will have the necklace.

Take it back to the mayor and she will assign you one last task: defeat Whipser's brother in a duel. For this you will have to go just past windmill hill. Defeat him and retrieve his helmet as a newly-acquired trophy. Now return to the mayor and she is yours for the taking. For those that choose not to take her dark heart, the lady near the jail is a safer option.