I would say ‘ These sites (Red Square and the Bolshoi Theatre) aren't popular among Muscovites because they are already very familiar with them’. Tiresome means annoying or frustrating, and does not really apply here. Local people don’t dislike these places, but they don’t excite their interest because they already know them well.

In addition to your sentence not being very descriptive, the Bolshoi theatre isn’t a ‘site’ . It could be a ‘sight’. A ‘site’ is a location where there is something, e.g. a building site is a place where there is a building. Red Square could be both a ‘site’ and a ‘sight’ I think.

"Sites" is correct, but did you perhaps mean "boring"? Maybe you could say, "These sites (Red Square and The Bolshoi Theatre) aren't popular among Muscovites due to the fact that living near historic places for one's whole life can often desensitize a person to the awe of these locations." Or more simply, "...........................because they've become jaded to these locations having seen them countless times." I had a similar experience in Istanbul. I used to see the Hagia Sophia every day when I'd be working and after just a year, I was already jaded, haha.

A place can’t be tiresome.