The only grave I visit on a regular basis is that of a friend of mine who was the first female graduate of one of the US service academies to die in the line of duty. She is buried at Arlington National Cemetery across the river from Washington D.C., and whenever my travels take me to DC, I spend an hour or so paying respect to her courage. I also walk through that area of the cemetery, which oddly is mostly graves from WWI, and say each name as I pass, to pay respect to those who gave service to our country. I feel as though as long as their names are spoken, their sacrifices are honored.
People visit cemetaries for more than one reason. I definitely understand you visiting this friend's grave. Arlington must be a very moving place to visit. I have seen it on TV and in movies, and can only imagine the feelings one must have walking through it.
I, too, walk through war memorial cemetaries, reading the inscriptions and paying respect to those who died in our country's service. So many of them were so young, especially those who died in WWI. But this is done to remember the horror of war and to pay respect and as a private tribute to those long-dead whose sacrifice should be remembered but who who might otherwise have no-one else to note their existence. Lest We Forget!
I also find it very interesting walking through old cemetaries, especially in country areas, reading the notes about the lives and deaths of those long gone. Standing there reading their memorial stone we are linked in place if not time to events which occurred decades, even centuries ago. (We - my culture, anyway - have such a short history in this country; it must be amazing to live in a country where you can visit places your ancestors lived many hundreds of years ago.) Standing before the grave you can close your eyes and "feel" something of what it must have been like in the time when that person's family were there laying them to rest so long ago.
But I think these activities are quite different from visiting the grave of someone I personally knew and loved. I don't want to revisit the sadness of their death and don't need visit their grave to remember them.
And the fact that a lot of my relatives are cremated rather than buried makes a big difference to attitude, I think. Some of them have been scattered to the four winds in obscure places that were of significance to them.
It's a personal thing, and there's no right or wrong about it, in my opinion.