Caveat: I’ve really not been out that much since the pandemic.
For Gastropubs you could try The Scran and Scallie. It’s in Stockbridge, which is in neither of your neighbourhoods, but you could enjoy a walk on the Water of Leith to or from there. But maybe expensive.
You could also try The Outsider restaurant on George IV Bridge. It’s a nice set up and there are some good views.
For regular pub (but if the weather’s nice you can sit outside on the water there is Teutcher’s Landing in Leith. Not expensive.
I don’t know if The Cloisters is serving food (they did pre-pandemic) but it would be a nice place to visit for a drink. (It’s in Tollcross).
A bistro on Dalry might fit the brief for close to West End. It’s called First Coast and it’s really nice. They change their menu every week.
(So far with the exception of the Outsider I’m avoiding the Royal Mile, but usually because I avoid that area if I can at all.)
I’m trying to remember if I’ve had any Middle Eastern food here that sticks with me. I’m sure there’s good stuff, I’m just blanking. I’d love to try Baba myself. But if you’re willing to go South Asian, there’s Dishroom and Mother India.
I’ll continued to have a think.