I see the ship docks at Newhaven, 0800 to 2200. The dock is very close to the retired Royal Yacht, Britannia. For an active person it's a 15 minute walk. I'm sure the SS "VIP" excursion will be silly expensive so if you'd like to visit Britannia (and you really should - it's magnificent) either walk or get a cab. If you are ex-military, entrance to the yacht is at a lower cost.
From Britannia you can get a bus (I forget the route number but Google maps will tell you) from right in front of the building to Princes Street where you'll find the Scott memorial, Scottish National Gallery (free entry!) and can walk across to the Castle, Royal Mile, Holyrood House. And after a good day's foot-slogging get the bus back to Newhaven.
Whatever you do I'm sure you'll enjoy Edinburgh. It's a fine city.
You also get to visit my old hometown of Belfast!
Looks like a great itinerary.