Go to the Dungeons! They say they’re haunted….well I never experienced any ghosties, but it’s certainly creepy down there!

Go to the National Museum of Scotland. Build a walk around it. (Here’s a street map.) Edinburgh is a wonderfully walkable city. You can combine it with a visit to Princes Street in one direction and a walk down the High Street (the Royal Mile) in the other. There is so much to see and do in that space, including little museums and pubs in the side streets, that you will be entertained for more than a day.

I stayed on the Royal Mile when I was there last.

Try the Whisky Heritage Museum, the National Gallery and (as @Jeruba said), the National Museum. If you’re looking for a really fancy pants dinner, there’s an amazing restaurant on the top of the National Museum. reservations are preferable.

Also, go to the Mussel Inn. best mussels you’ll ever have.

Oooh, I had dinner at the Mussel Inn! I think! In Rose Street? It was wonderful.

I also dined at the Abbotsford and had (yummm) haggis with neeps and tatties and the best bread pudding I’ve ever had.

Definitely go on the Free Tour—it’s three hours, but worth every minute, really excellent stuff. Eat haggis, as @Jeruba suggests; don’t think about it, just do it, for it is delicious. Um… yeah. We were only there for one day, and spent a lot of our time on the tour. Holyrood House is nice, if you feel like springing for it.

Ach, I meant the National Gallery, on the Mound, just about in the middle of the map I linked. I’m sure the Royal Museum in Chambers Street is wirth a visit too. That’s just not what I was referring to.

The local’s advice:

If you’d like to check out an incredible pub, I’d recommend Sandy Bell’s which is very close to the Chambers Street Museum. Go there one evening and enjoy the incredible folk musicians that seem to practically live there having sessions live in the midst of the pub crowd. Best authentic experience of Scottish trad music you’ll find in Edinburgh.

I’d also recommend picking a nice day and climbing Arthur’s Seat, the extinct volcano near the Parliment building – the views from up there are incredible.

Lastly, if you need to get anywhere further than the center of town, the bus network is quite excellent. Their website is here and although there are currently roadworks on the main street in Edinburgh (Princes Street) to make way for the new tram system, the buses are still running smoothly. If you have an internet connection while you’re here, you can use not only their online timetables but the Bus tracking system which will give you live departure times (there are live signs at the majority of the stops in the city now, and their site just hooks into the same system).

If you have any questions / want more recommendations drop me a comment!

Oooh, also if you end up being around on a Saturday morning and are staying in self-catering, visit the Farmer’s Market – if only for a hog roast sandwich!

And a further note on the bus tracking system – if you find yourself at a bus stop that has no tracker sign installed, then use http://liveb.us on your mobile device.

Disclaimer: i built that, but it’s really useful, honest!