Musselborough as in near Edinburgh?

Go on the ghost hunt tour of the old haunted city.

Swim is also a good idea - you could impress her with some fancy diving off the 10m board at the Royal Commonwealth Pool.

Lunch on Royal Yacht Britannia

Day trip to Glasgow / Loch Lomond (it has been said that the train to Glasgow is one of the best bits in Edinburgh!), maybe a trip on the West Highland train to Fort William / Oban

Canal boat trip with picnic hamper, crystal classes, linen tablecloth etc.