Also, as many people have said, Edinburgh is very nice but you could visit a city anywhere. It's not worth going all the way to Scotland for. If you do go, I'd recommend

Circus Lane - it's just a residential street but the buildings are really nice and there's a lot of plants and flowers there.

Prince's Street: main shopping area, also next to a big park. When I went there was a market outside where I bought some spicy sauce from Bonnie Sauce Co. - veery good and I buy more whenever I can. It's also a good hub for public transport

Cockburn Street - I think this is the sort of place Americans would call charming - it's kind of an old cobbled street, wiggles up a hill with lots of small shops and cafés on either side. Lots of Harry Potter stuff here if you're into that. I also think this is the street where there's a weird split level thing going on, where there's kind of a balcony street about four stories up overlooking the main street. (if you can't tell, it's a while since I've been here and my memory isn't great).