The desire to locate Har Sinai is the simple curiosity that we all have. There is no residual kedusha on Har Sinai, and going there will not accomplish anything in terms of our Avodas Hashem. Satisfying curiosity is a form of pleasure, and not a bad thing, but it does not become a mitzvah just because it feels good. If there was anything left at Har Sinai, there would have been a mesorah to go there, visit, and what to do there. There is not.
As for the stones that are sold with the image of a bush on it, that exist no matter how you cut it, there is a mesorah on that brought down by R’ Yaakov of Emden, and references the Medrash that states that this is Har Sinai. It is nice to own “a piece of the rock”. But it is not a דבר שבקדושה and one is not better by having one. Our connection to Torah is through learning and studying it, and following the guidance and instructions contained therein to govern our lives. The Torah is the gift, and goes wherever we go, and brings השראת השכינה to everyone who learns it. The original address is irrelevant.
The case of the מקום המקדש is obviously different, and it maintains its status as a מקום קדוש for eternity.