Do any characters just wander the parks anymore? I’d love to have a couple character pics, just for the novelty, but we are two adults so don’t really want to spend time lining up for a meet and greet.
If not, anyone have suggestions of the quickest character experiences throughout the parks! Not at all picky about which ones 
You might want to look into a Disney Visa. One of the perks is two locations for a meet/greet with the card. The waits are usually very minimal. The card has other perks as well.
As for random character spotting, we did VERY WELL at epcot around the IG. We saw a few stationed right there, near the friendship boats waving ppl over for photos, and we also seemed to run into a few, that were probably entering the park via the IG.
Very few just wander the parks - like @seebee says, there is sometimes characters in training in Epcot, but can be very hit or miss.
Shortest lines are just after RD for characters that meet that early - at Epcot you can hit Baymax after doing TT or Soarin, HS you can get Olaf or Mickey/Minnie after doing a few of those headliners. At MK, Daisy/Minnie and Goofy/Donald are stuck way back in Storybook Circus, so if you get there when their meet opens at 10 (? I think - definitely not at RD) it will be a very short line. You can also sometimes get a SD FP for Mickey and Minnie at AK, but even with FP it can be a 15 minute wait.
Saw Mary Poppins all on her own wandering in Epocot and on another trip, just starting up her meet in MK. But on both occasions we were too shy to say hello!
No wanderers.
I would meet Mickey - duh - preferably the Town Square one. I would also meet Sorcerer Mickey (he’s my favorite) in HS. Love meeting Buzz and Woody. Tink was surprisingly loveable. Those are all long lines though.
As @megan484 said, the Storybook Circus meet and greet is a blast and if you’re there at 10 (which, as she said, is when it opens), you’ll have a VERY short wait. A couple of trips ago (2015), we were there a bit before 10 so we wondered around the Big Top Treats store next door and walked out to stand by the M&G about 5 minutes before 10. As we stood there, we started hearing banging on the doors from inside and a few gloved hands popped out from the doors- they then swung open and all of the characters (Minnie, Daisy, Donald, and Goofy) came out and grabbed us. It was such a fun experience.
Oh! There’s a lot of characters wandering the parks. Just not the ones you’re looking for.
My favorite character experiences this last time were Buzz and Woody at DHS, Chip and Dale at Frontierland in MK, Tinker at Town Hall on Main Street in MK, and Anna and Elsa at Sommerhaus Norway Pavilion in Epcot.
We did quite a few but those were exceptional, IMO.
So I haven’t been to Disney since the meet and greets were basically find the characters on the street and snap a picture. What are these special meet and greets like?
Buzz and Woody were just “on.” My granddaughter asked if she could push Buzz’s reset button and he was trying to convince her to press the laser button and Woody went into a panic and their handler had to tell Buzz to behave that he knows he’s not supposed to do that inside.
Chip and Dale were adorable. Chip kissed my hand, Dale helped granddaughter put the hood to her shirt on and it was just fun. Interactive.
Tinker took a look at my granddaughter’s BB8 shirt and was all “Wow, you made your pixie dust into a picture.” Very sweet. Very kind.
Anna makes you feel like you’re her long lost cousin. You’re family.
Would you consider a character meal? Food and characters and air conditioning! I love CP for breakfast or lunch. You get to meet Winnie the Pooh, Tigger, Piglet and Eeyore. I hear good things about GG at Epcot, where you meet Chip and Dale.