Had a great day yesterday checking out a lot of the suggestions in this thread.
I could only get a park reservation for Epcot, but parked at Studios and started with a hop on the Skyliner from to Riviera to check it out. I had thought that I might stop at either Le Petit Cafe and sit in the Voyageur's Lounge, or go to Primo Piato and have a glass of wine and charcuterie or cheese plate. I must admit to being disappointed in the entire vibe at Riviera. The Voyageur's Lounge was packed - looks like it would be a cozy place to sit if uncrowded. I thought Primo Piato was less than inviting. It wasn't crowded but seating looking uncomfortable and the charcuterie/cheese plates were not appealing looking. So I hopped back on the Skyliner to Epcot.
I mainly wanted to check in at Epcot so I had flexibility to enter Studios later if desired, so I did not spend much time there - very crowded. I really wanted to stroll back through the Boardwalk area and check out some of the other suggestions up thread.
First stop, Beach Club. I found the Solarium and what a lovely surprise! Only about a quarter full with plenty of small tables alongside the windows, quiet, tucked away. Just perfect! So I went into the Marketplace and grabbed a single serving of red wine and bag of chips (I wasn't hungry enough for more having had lunch at home before arriving), then settled in to a window table in the Solarium and read on my Kindle, watched some streaming video with my headphones, and chilled.
I walked through the Beach Club and took a peek at Martha's Vineyard which was open by now. Loved it! I didn't stop this time, but it will be on my list for a future visit. Lots of cozy seating and the lounge menu looks appealing.
Next stop, Yacht Club. I loved the vibe of the Crew's Cup Lounge, the seating looked great to tuck in and relax for a bit, but the menu wasn't that appealing for what I'm usually looking for. Unless maybe I'm in the mood for an Irish coffee, but this is rare in Florida, lol. The menu is more appealing at the Ale & Compass lounge, but I found the seating area to be less appealing when trying to tuck away solo and discretely read for an hour or so.
I then walked to the Dophin, entering on the level of The Fountain which was not at all appealing. The main floor lobby was packed with hundreds of people attending a reception for some kind of business conference. I have been to the Dolphin lobby years ago where I could stop for a moment and sit on a couch, maybe even with a piano player in the lobby, IIRC. But this day it was overrun with people. I took a peek at the various quick options like Fuel and Picabu but neither fit the bill. I tried to take a peek at the Blue Zoo lounge or Shula's lounge but both seemed inappropriate for a late afternoon pop-in wearing shorts.
Last stop was the Swan hotel that seemed to also be hosting the business reception spilled over from the Dolphin. I walked past Java but if I were to choose, I think Fuel at Dolphin was a better option than Java.
So to summarize, the Solarium at Beach Club was perfect and I can see enjoying Martha's Vineyard another time. I also plan to walk around the Boardwalk side next time and maybe try AbracadaBar or sit at the outdoor seating area of the Inn. For any days except the weekend, I agree there are several areas in Epcot World Showcase where one can tuck away off the beaten path, but less so on the weekends. Morocco has some tucked away spots, as does Japan.
Thanks to all who made suggestions and feel free to add to it, also for the MK/AK and surrounding resorts.