The Gedolim by and large (with the exception of Rav Elyashiv) are very accesible. And even Rav Elyashiv, if you just want to see him, you can, just you cant get close to him so often.
But the rest, Rav Chaim, Rav Shteinman, Rav Michel Yehuda, Rav Vosner, Rav Scheinberg, Rav Nissim Karelitz, Rav Shmual Auerbach – you can get time with. if you need more info, let me know