It is true that locals tend not to visit historical landmarks and museums in their respective towns/cities, however, they are mainly visited by tourists. There are many reasons for this, mainly its because locals are always working and get no time off, whereas tourist are on vacation and have the time to visit these sites.
It can be argued that visiting these landmarks or museums can be very expensive, especially for locals. Most tourists on vacation are willing to spend the money and they do not consider it expensive but for locals however, that is not the case. A good example of this could be the historical sanctuary of Machu Picchu, most locals there are working and not visiting, due to expenses among other reasons. The lack of time is another reason locals choose not to visit, they are overworked and whenever free time is available, they choose to rest. Compared to a tourist, whose main goal is to visit these ancient sites.
There are many ways to captivate local people into visiting these sites. Prices are one of the main issues for locals, the way to go about this is to lower the rate of tickets for local people. For example, the Pyramids of Giza in Cairo, Egypt. There are a different set of prices for westerners, such as people from Europe and the US. Meanwhile, locals and Arabs pay less to visit the pyramids. Another issue would be having no time to visit as locals are being overworked, and whenever they find time off, they may choose to rest instead of doing activities.
In conclusion, I truly believe that if local people are given the time they need to rest from work and a bit more, they would most definitely visit the sites in their cities.