a whole day in Edinburgh - what to do?

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On Sunday my DP is working in Edinburgh. Im going to hitch a ride and keep myself occupied in the city until he finishes. I'm quite looking forward to such a long sint of alone time to do as I please. I've been to Edinburgh for the Christmas markets, rugby and a bit of shopping but I've never done the museums or touristy stuff - or had to kill such a long amount of time there whilst completely sober.

I'll be kicking about from around 8am to 3pm. Anyone got any "can't miss" recommendations? I reckon I'll end up sitting in a coffee shop with my book from lunchtime, which I'm OK with but if I can find some good stuff to look at instead, all the better.

The national museum of Scotland is always a shout - especially if it's miserable weather!

Agree the Museum of Scotland on Chambers Street is awesome - loads to see (and free to get in). If you like art galleries there are plenty in the city centre (with coffee shops for a snack) - google National Galleries of Scotland. Childhood Museum on the Royal Mile - and just the RM in general - go for a wander down it and maybe do Mary Kings Close while there. Obvs you could do the Castle and/or Holyrood Palace if those float your boat (both expensive to get in). Down by Holyrood Palace, you also have Dynamic Earth which is worth a visit, and the Scottish Parliament too. At Waverley Station you can get a tourist bus to go round the city and jump on and off at various tourist spots - a good way to get a feel for a fab, interesting city (yes, I’m biased). Have a fab time

I would go up Arthur's Seat for an amazing view and then for a walk on Portobello beach - easy bus ride from the city.

The new st James centre is worth a wander if it rains, and there is a food market called Bonnie and Wild with lots of choice for lunch. I went there when DH was working in Edinburgh and I spent the day wandering

Yes to the national museum. Also the art gallery is fun.

I like Mary King's Close; the old streets under the existing city which were shut up during the plague. Also Gladstone's Land, the 17th century house on the Royal Mile nearby. And the Camera Obscura (and World Of Illusions) is nearby too and really interesting.
Visit the Grassmarket and Victoria Street, just off the Royal Mile, for interesting independent shops and if you go to the National Portrait Gallery on Queen Street, walk a few minutes down Leith Walk to Valvona and Crolla, the famous Italian deli. It has a coffee shop too. Broughton Street near there has nice little restaurants and a lovely Swedish bakery. And a great wool shop if that's your thing.
If you're more of an outdoorsy person the Royal Botanical Gardens are lovely for a walk round.
You can walk more or less anywhere in the centre of Edinburgh. Have a great day!

Holyrood House
Edinburgh Castle
Scottish National Gallery
"New Town"
If lots of time, get the bus out to Leith for the Royal Yacht Britannia.

It takes days and days to see Edinburgh properly - you don't have enough time!

Thanks all, some fantastic suggestions here which I will definitely make use of! I'm usually the sort to formulate a plan but I think I'll go wild and just wing it; see where my feet take me to in no particular order for some of the above highlights.

Giant pandas at the zoo

Definitely check out Stockbridge - some lovely coffee shops and inverleith park leads to the botanic gardens.

Botanics definitely - hop on a no 8 bus heading north.

Scottish National Portrait Gallery.

Mary Kings close is great.
There is a market in Stockbridge on Sunday. You can walk along the river of Leith from there to Dean Village .