It looks like UNESCO uses the term “Property of Cultural Interest” more often than other alternatives (“Asset of Cultural Interest”, “Cultural Interest Asset”), as seen on the following unesco.org pages (a total of 9 hits using the advanced google search to look only on unesco.org pages).
www.unesco.org/culture/ich/doc/.../00172-Nomination_form.do...
…the Island Council of La Gomera began a Declaration of a Property of Cultural Interest report in favour of the Silbo Gomero…
whc.unesco.org/document/1076 –
have been declared to be a Property of Cultural Interest (Bien de Interés Cultural).
www.unesco.org/culture/ich/doc/.../00259-Nomination_form.do...
With regard to cultural heritage property and property of cultural interest, the following obligations and competences are set out:…
Another option I like, but which may not be the most accurate from a UNESCO perspective:
www.hotelazar.com/entorno6_eng.html
At the bottom of a lovely valley surrounded by pine trees is Gata, which has been designated a historic site of Cultural Interest.