Ohhhh congratulations :)

Where about in Leith do you plan to marry?

I would second the recommendations above to climb Arthur Seat, amazing views of the city, and an opportunity to take time out and enjoy the natural beauty. Definitely my favourite spot within the city, and I never tire of being there.

Edinburgh Castle is over priced – you can still enjoy the views of the city from the esplanade, without forking out the entrance fee.

Witchery Tours – Thumbs up. Good fun, and great to snuggle to if things get too scary ;)

Walk around the old town, down the Royal Mile soak up the atmosphere, peak down the closes.

If you are a chocolate addict I would highly recommend http://www.plaisirduchocolat.com/ – Plasir du Chocalat. Try the hot chocolate I dare you! Or manage to walk past their cake/sweet counter without drooling. If you want to spoiled this is the place.

In and around Leith…. I love sitting out at the shore on a Summer’s night with a glass or two of wine. Walk around that area see what takes your fancy.
http://www.royalyachtbritannia.co.uk/ – Royal Yacht Britania. Having been a resident of Leith for more years than I care to remember I haven’t yet been to Britannia. You can view/board the ship from the local centre http://www.oceanterminal.com/ – Ocean Terminal.

Restaurants – If you want to really treat yourself on the higher end of the price range there is http://www.waterfrontwinebar.co.uk/ – The Waterfront.

Coming down the range…..Ship on the Shore http://www.bestpubs.co.uk/layout0.asp?pub=143223