A day is plenty for Edinburgh and you do not have to get up that early and spend all the day sightseeing. Main tourtist stops are:

a) Edinburgh Castle (best leave this for mid-day as they shoot the cannon at 1pm
b) Britannia (see how the Queen sailed around the world and realised how antiquated it was)
c) Holyrood Palace to visit the Queen's Scottish Palace
d) take a bus tour around town but as you can see there are not many stops around Edinburgh

Try to book somewhere like the Witchery for dinner well in advanced of arriving.