Congratulations on your upcoming wedding!
Since you won't have quite a week, you can easily base yourselves in Barcelona and take a few day trips. I really enjoyed Tarragona and Girona. The train rides were frequent and easy, and there were plenty of things to do. Tarragona is coastal and has some fantastic Roman ruins. Girona has a beautiful old town. Getting lost in the small winding streets would be romantic. In Girona, my husband and I had a picnic lunch in a local park, and we ended up finishing off an entire bottle of cava!
Speaking of cava, we took a day trip to Sant Sadurní d'Anoia and visited Solà Raventós, which is a small cava maker. I booked in advance. We really enjoyed our tour/tasting, and they also booked us a nice lunch at a local restaurant. We went in December, and the town was very sleepy. In order to get the most bang for your buck, I would try to visit a second winery or research when they have their market days.
We've stayed at H10 Racó del Pi two different times. It's on the edge of the Barri Gòtic, which makes it nice for evening walks. One stay, we had a little balcony. We would have drinks out there and watch people walking by on the street below. It is very near Basílica de Santa Maria del Pi, which offers cozy guitar concerts. I would also recommend the Anakena House Bed and Breakfast. It is in the Eixample neighborhood, which gives you access to lots of restaurants and bars.
There are loads of lists out there about top sights in Barcelona, so I'll mention a few that are less likely to be mentioned. Parc de la Ciutadella is a nice green space. You can rent rowboats, and I always find that activity to be romantic. If you want to visit a market with actual locals, check out Mercat de Santa Caterina. You could cobble together a meal here and then eat it in the park. (Can you tell I love picnicking?) The beach can easily be accessed within the city. I've never done a sunset cruise, but I think that would be quite nice. Montjuïc is a lovely area. We like taking the telefèric to the top and then wandering our way down. Again, we would bring a picnic and eat it somewhere along our ramble.
Also, Sitges is another day trip option. It's got lots of coast line. Honestly, I thought it lacked in sights. However, if you are just looking for walks on the beach and plenty of restaurants/shops, then this is a good pick.