Personally, I've always liked the stand alone plateau to the east of Idyllshire which gives you a great view of the cenotaph and the practically floating island that it's on. Day or night the music there is serene. Other than that, night time in The Lochs is pretty great on the southern tower looking out over the endless clouds and canyons.
I also rather enjoy Churning Mists for its music, and its look during the thunder weather.
Can't go wrong with Ruby Sea either. It has several places that I love to chill. First and foremost the Reisen Shrine with the Auspices. Then Tamamizu with the Kojin. Other than that, I like to sit underwater near the Easter Island head over near the ravine the that leads down to Shisui of the Violet Tides.
In ARR areas I have a great love of the western half of Upper La Noscea for its music, but also for the view from the highest point atop the menhirs or whatever they are that stick up out of the hill that leads to Outer La Noscea.
As for Shadowbringers areas... Kholusia during the day for its music, makes me feel like I'm sitting outside in the countryside near where I've lived for most of my life, only the smells of cow pastures are absent, so it's a bit better haha. Other than that, the portions of The Tempest where you can look out over faux Amaurot are kinda nice, as is the dark blue atmosphere of the entire zone.
As for dungeon areas where you can go yourself unsync or you can stay behind after a dungeon run... I love Holminster Switch's first 1/3rd it reminds me of the woods behind my house. I like being underground, so all of Malikah's Well is a real good time for me, and I like the area and music too, feels very serene to me.
The Burn takes the cake for atmosphere to me. Love the bagpipes song remix of Praetorium that goes on there, and I love the giant dead sandworm spot the most. You can solo it with relative ease on any tank too.
Sohr Khai has a lovely atmosphere at the very end after you fight with Hraesvelgr.
Keeper of the Lake has a nice view from the lead up to Midgardsormr's arena.