Royal Mile Whiskies in Edinburgh City Centre has some good bourbons (check their website), but it would invariably be cheaper if bought in the USA. They may also have Sazerac - if they don't, then I think Valvona and Crolla (Elm Row, Edinburgh) has some. My guess is that East Lothian proper would not have a great selection of bourbon.
For my money, though, you could do a lot worse than offer a bottle of Bookers (c£50 in The Whisky Shop - various branches in central Edinburgh). It is cask strength, has enormous taste and finish so it will last for ages. It is sweet and syrupy, but has an enormous range of flavours - warm corn, herbs, fruitiness, charcoal. These notes are just based on memory - every time I try it, I get something new. I also find that I can still taste it quite clearly the next morning, regardless of what I have eaten or drunk in between.
You might also want to take a Glencairn tasting glass to make sure your spirit of choice is shown off to best effect.
Hope you have a great visit.