'Unique' experiences in Barcelona

"Unique" is a pretty subjective term, but I notice you didn't include Saint Pau in your list of sites. It's a short walk from Sagrada Familia, with maybe 10% of the crowds. Montaner isn't as famous as Gaudi, but I like him better.

https://www.catalunya.com/recinte-modernista-de-sant-pau-17-16003-300?language=en

You might enjoy a Devour tours food tour. They blend history, culture, and you test different foods all around ours began at a wonderful market it was a great way to learn what we’d want to eat more of as well as getting history and an enriched few hours of our day.

The Mares museum is quirky and worth a visit if you want to avoid the more obvious options. The Picasso Museum can be unbelievably crowded (think of the photos you may have seen of the Vatican Museums), so I recommend it only to serious fans of Picasso. The Miro Museum and the MNAC were very pleasant art venues when I visited them in 2016. They are not undiscovered, however.

The Caixa Forum, an arts/cultural center, is located in a repurposed modernista factory building.

You should consider walking back downtown through the Gracia neighborhood after you visit Parc Guell.

The Ramblas is not worth a special effort. You'll probably find yourself on it once or twice, because it's a main road, but in my opinion there's nothing special about it except the presence of pickpockets. I have no clue why Rick still recommends it.

In addition to experiences on your list, we visited Palau de Música Catalana. We enjoyed a guided tour. Both the exterior and interior are breathtaking.

Ride the cable cars up to Mont Juic then walk down and stop at the Miró Museum. A lovely museum with some wonderful views and art.

Have a coffee or hot chocolate with churros at Xurreria Laietana https://www.tripadvisor.com/Restaurant_Review-g187497-d2216792-Reviews-Churreria_Laietana-Barcelona_Catalonia.html

I can personally recommend:

Parque del Laberinto de Horta: A 18th-century neoclassical garden on a former palatial estate. It's not very well known with tourists but is very beautiful with numerous sculptures of Greco-Roman mythology along with a number of fountains, springs, and pools. In the center of the gardens is an English style hedge maze.

Hospital de Sant Pau: A Gaudi-esque modernisme complex built in the early 20th century as a hospital. It's about a 10 minute walk north of La Sagrada Familia. It's now a museum and has been named a UNESCO World Heritage Site. Sant Pau has significantly less tourists than La Sagrada Familia.

MUHBA Plaza del Rey underground Roman Ruins of Barcino

Tibidabo the oldest amusement park in Spain plus the best views of the city.

Thank you everyone for the wonderful suggestions. There are several here that I will be looking into. I truly appreciate the feedback and value your experience/expertise!