The museum is good, and free.
Ghost bus is sort of fun if you want to hear the stories with a mini bus tour thrown in. Otherwise there are loads of ghost tours.
Mary King's close is an interesting visit
https://www.realmarykingsclose.com/
Carlton hill is a quick walk from Waverley and has great views.
Arthur's seat is easily walkable and again a good view.
If you are up for it you can get a train to Dalmeny (~15mins) and get a boat tour under the Forth bridges and to Incholm Island if you want to visit the Abbey.
https://www.maidoftheforth.co.uk/ or
https://www.forthtours.com/
If it's your thing then Edinburgh gin have a tasting tour
https://www.edinburghgin.com/visit
Lind and Lime also have a one a bit further out
https://www.lindandlime.com/thetour both are great IMO but Lind and Lime give you more free gin and I like their flavour profile more
The Zoo is...a zoo. Nothing special if you've been to a big one before.
As for food there are the usual chains, I do like Cafe Andaluz though but I'm a tapas fan and its just a chain.
Dome is fancy but you'll need to book.
Witchery is expensive and I've never been but hear good things.
If you're an Avengers fan go to Cockburn Street (next to the station) to see where a Vision/Wanda scene was filmed, also they were at the station itself. Thats pretty niche though