The Park Guell(spelt "Park"for a particular reason) springs to mind immediately for purpose indicated-designed by Antoni Gaudi,extraordinary,atmospheric park offering privacy in unusual setting-Unesco World Heritage site and famous worldwide-Bus Turistic stops here
Other unusual locations would be unfinished Sagrada Familia cathedral-a few minutes privacy could be snatched here but really only suitable if an immediate reply expected-,the Olympic stadium if you are both sports enthusiasts or the Camp Nou football stadium if you are both soccer fanatics.The Parc de la Ciutadella is a pleasant,fairly busy park,with a small zoo on site, very close to city centre,attractive fountain in park,definitely suitable for purpose,close to bars for immediate celebratory drinks if response positive,but without"wow! " factor of Park Guell.