There is a guy Yankelowitz who does a very unique tour of as many gates to Haar Habayis as possible.
I've done this tour with him at least three times, very good, He does many other tours: The israel museum with a torah perspective... Quite a unique person. He was the one who convinced Rav Belskey to wear tcheles, s an expert in the ksav in old sifrei torah.
I would recommend to get a hold of one of the good guidebooks to kevarim. I personally use "HaMekomos HaKedoshim" by Rav Yechiel Michel Stern (from Ezras Torah), and "Kadmunienu" from "Vaad Lehatzolas Kivrei HaKadmonim in E"Y". They provide accurate directions, and background on who each person was, how we know he's buried here, and some torah that each one said. Available in many seforim stores here in Israel, but worth to get a hold of, and read in advance.
My recomendations:
Abaya and Rava. aside from the opportunity to daven there, the view is amazing, prob top five in Israel.
When you decide to go to a particular kever, check who is nearby.
The Chida is at the enterance to Har Hamenuchos. Fof har hamenuchos and Har Haziesim you prob NEED either a very good map, or a guide.
Figure out which Tanaim, Amoraim, ext.. are meaningful for you to go to. Is it the talmidie habesht in tveria and tzfas, a particular navi...If you're a segula person which segula are you looking for ? (amuka...)