What to do after sleeper arrival?

[whattodointhemorning]

We're getting the sleeper up to Edinburgh, arriving on Saturday morning and looking for suggestions of what to do when we arrive to fill the morning, to avoid just wandering round aimlessly.
We will be meeting people for lunch and staying within Edinburgh, so, looking for something that is walkable and not hugely expensive (free if possible).
We will get a basic breakfast on the train (think it's a bacon roll or similar) but that doesn't preclude getting more food!
Museum of Scotland was my go to but that doesn't open till 10 and we get in at 8.
There will be me, DH and DS 11.

Weatherspoons Round the back of the station is open from 8.00am. The National Gallery opens at 10.00 and is across the square. Personally I’d recommend Dynamic Earth which is amazing.

What square? The National Gallery is on Princes Street.

OP there really won't be much open until 9 or even 10. If it's a nice day you could wander up Calton Hill maybe. There are lockers at the bus station if you need to store luggage, stock up on pound coins!

I think you have to pay extra for breakfast on the train. If you want food then Loudons opens at 8 and does a lovely breakfast menu. Loudons - New Waverley | Breakfast, Brunch & Lunch in Edinburgh Cafe Nero, Costa and Pret a Manger in the the station will also be open but none of them have much seating space.
I would take the opportunity to explore the Royal Mile while it's pretty quiet or walk up Calton Hill if it's a nice morning, then head to the National Museum or Dynamic Earth.

Thanks all. Dynamic earth has always been on the to-do list. However, at £50 for 3 of us I think we'll probably leave that one until we have a full day free esp. as the first time slot they have is 10.30, then we would have to hoof it across town to meet people for lunch.
Had forgotten about the Spoons at Waverley; not exactly gourmet but normally not too busy and fairly cheap. Maybe we'll stock up on newspapers or magazines and hang out there until MoS opens.
Loudons looks really nice though, I'll see if I can convince the budget holder to splash out...