Where is the chemist's?

Hint 1 of 6:

Did you talk to the flower girl outside the bar?

Hint 2 of 6:

Buy a flower to get her to talk to you.

Hint 3 of 6:

She'll tell you about Sarah's secret admirer.  Now you need to find him.

Hint 4 of 6:

Someone in the bar has probably seen him.  Ask around.

Hint 5 of 6:

The publican will give you the information if only you prove you're worthy.

Hint 6 of 6:

Ask each of the men in the room to play darts (right to left).  When you beat
all three, you can play the publican for the information you need.