Edinburgh is close enough to here that we don't do any of the tourist things... don't venture into town that often either.
Things to see:
Edinburgh Castle - the most popular fee-charged visitor attraction in Scotland by some considerable margin, they can't all be wrong, can they?
Mary King's Close - a tour in the subterranean world of the Old Town where the poor lived and died (and when plague struck they just bricked up the closes)
There are a number of guided walks - the Rebus one is a good one, and if you're particularly lucky, Ian Rankin might show up - he does do that from time-to-time.
The Scottish Seabird Centre - just a short train ride away at North Berwick (about £8 return)
Trip on the Forth out to the islands (departs from under the Forth Bridge at South Queensferry - not been on it for about 25 years, so no idea on when it goes or what it costs).
Rosslyn Chapel - it's get-attable (by bus - Lothian route 15 - it's in Roslin confusingly) and you've read Dan Brown's Davinci code so really you ought to go, probably.
<!-- m --><a class="postlink" href="http://www.edinburgh.org/" onclick="window.open(this.href);return false;">http://www.edinburgh.org/</a><!-- m --> is the official visitor portal for Edinburgh & the Lothians.
Tip/Watchout: Lothian Buses (ie. most of the buses in Edinburgh) do not give change under any circumstances, so if you jump on and only have a £20 note, your £1.20 (at least it was £1.20 last time I jumped on one) fare will cost you £20). The fares are flat fare and a day pass is about £3. Also all Lothian Bus drivers are miserable bastards and may pretend not to understand your non-Edinburgh accent. You can also be a complete numpty and buy a 20-journey carnet with a massive discount of 0%, not sure why anyone would want to pre-pay Lothian Buses though.
Conversation starter: Mention to as many people as you like, especially shopkeepers on Leith Walk how much you love trams and can't wait for the number 22 bus to be replaced by a tram.
EDIT - Totally forgot about the Scottish National Portrait Gallery, the National Museum of Scotland, HMY Britannia (it has a bell on it I'm sure) - and of course the shed-like structure that is the Scottish Parliament.