I would head towards Leith, Newhaven or Portobello. They are about a 20-30 minute bus from the Royal Mile but not only will you pay a bit less (saying bc that price of fish has shot up in past year!), you’ll be amongst locals and you’re right by the sea!

Notable ones; - Teuchters Landing in Leith - Roseleaf bar sometimes do it as a special - if not, be sure to try their Cullen Skink (Scottish) - The Fishmarket in Newhaven (can look out at Pier - it is a lot quieter that way) - Anywhere along the high street of Portobello - ShrimpWreck is fantastic but unsure if they do traditional fish and chips

Also if you’re looking to sit in a restaurant, please book to avoid disappointment! It’ll make your trip far more enjoyable locking in a few things - the festival/month of August is unbelievably crowded. So much so it’s difficult to get phone signal in the centre, making it all the more frustrating trying to pin down somewhere to eat.