I'm doing some research on shows that work well outside (not Shakespeare, thanks) and I am looking to do some research of some good outdoor productions you may have seen or shows that work well outdoors.
Into the Woods is an obvious one. I also saw an outdoor production of South Pacific that worked pretty well. 
I think most established shows probably CAN work outdoors, as long as it isn't super reliant on the claustrophobic feeling of being indoors - the same company that did South Pacific (Mountain Play) did Beauty and the Beast a few years later. All of their productions are performed in broad daylight - so when Belle gets lost in the woods at night, and then gets shut up in a dark, dingy castle, the effect is kind of lost. But that was largely because it was daytime, not necessarily because it was outdoors. Performing outdoors at night offers enough flexibility with lighting that it kind of doesn't matter where the show takes place. 
However, if you're looking for that "next level" quality of shows that are enhanced by being outdoors (rather than just "working" outdoors), then I guess it's best to look for shows that take place in nature, or surrounded by nature, right? The Seagull is another one that comes to mind offhand
Or you can have immersive/experiential shows that were conceived to be performed outdoors from the get-go - we've seen some of those during COVID times, naturally. There's the Voyeur show that's been running for a few months now, and there was Bill Irwin's "Busking Project" which was performed on the street. 
Seeing A Midsummer Night's Dream at the Delacorte a few years ago was one of my favorite theatergoing experiences ever. The show started when it was still light out, and night fell just as the characters were going into the forest. It was absolutely magical.
A little corny, but seeing Les Miz at the Hollywood Bowl was neat when "Stars" actually had stars in the sky!
I’ve always wondered what it would be like to watch SUNDAY IN THE PARK WITH GEORGE outdoors. Such as at regents park.
Understudy Joined: 3/21/18
		     			Bring it On on a football field 
Hands on a Hardbody 
Once on this Island 
Oklahoma! 
Anything Goes 
Into the Woods 
Cats 
Sunday in the Park 
Charlie Brown/ Snoopy! 
Chicago 
		     				
		     					
Hair, Carousel, The Seagull, Seven Brides for Seven Brothers, Hello Dolly!, Jesus Christ Superstar
Updated On: 3/17/21 at 01:02 PMI think it's less a question of what shows work well outdoors and more a question of what outdoor *venues* are best to do shows in.
Kad said: "I think it's less a question of what shows work well outdoors and more a question of what outdoor *venues* are best to do shows in."
 
Can you expand on what you mean by this? Why it it "more a question" of that? Seems like it's just 2 separate questions. It's true that a venue like the Delacorte, for example, is high-tech enough that you can pretty much do any show there, and it doesn't hugely matter whether the play takes place outdoors or not. And that might not be the case with every outdoor venue. But it still seems that some shows will feel more special, or get an added layer from being performed outdoors, regardless of the specific venue. 
 
On a separate note, I just remembered they did Ghost Quartet outdoors around a campfire some years back. I would've loved to see that. 
The Serenbe Playhouse in Georgia (current status is changing as entire staff was fired/laid off last June) did outdoor shows - but with a flair - like flying in a helicopter for Miss Saigon and having the Titanic set sink in water with the actors jumping into water.
Titanic:
 
 
qolbinau said: "I’ve always wondered what it would be like to watch SUNDAY IN THE PARK WITH GEORGE outdoors. Such as at regents park. "
I want to see SUNDAY IN THE PARK WITH GEORGE performed on the Île de la Jatte.
Call_me_jorge said: "I want to see SUNDAY IN THE PARK WITH GEORGEperformed on the Île de la Jatte."
 
That would be awesome! 
I was lucky enough to visit Ile de la Jatte about 6 years ago. The funny thing about Ile de la Jatte today is that it's actually pretty lovely, whereas Act 2 of "Sunday" implies that it became tacky and over-developed. Maybe it was, back in the 80s! 
 
Videos