Hey Henry,
I’d recommend Parc de la Ciutadella. It’s a lovely urban park where you can go for a stroll along the lake and have a picnic away from the busier areas. Montjuïc is also beautiful to wander around.
Some places off the main tourist trail include El Born neighborhood, cute taps com shops and squares. Also check out Park Güell at sunset when it’s less packed. The gardens at Palau de Pedralbes are gorgeous for relaxing. A bit outside the city, you two might enjoy Sarrià – it’s a charming village with nice shops and cafes. You might want to check out their official tourism site for more infor https://www.spain.info/en/destination/barcelona/ and this guidebook https://gowithguide.com/blog/tourism-in-barcelona-statistics-2024-your-in-depth-travel-guide-5731 This will give you more insight.
Hope you both have a wonderful trip! Let me know if any other Barcelona tips would be helpful as you plan your itinerary.