Pope Finis I
A couple of names with a long papal history which haven't been used for a while are Leo and Gregory. I don't know how much popes think about the previous holders of a name before selecting it--the last pope Leo was well-regarded but not so Leo X (elected 500 years ago in 1513). Maybe it helps if one or more earlier popes with that name was canonized.
There are some names which belonged to apostles which have never been used: Andrew, James, Philip, Thomas. There was an antipope Philip but he doesn't count.
Urban might be a good name, in honor of Urban II, who started the First Crusade, as a signal to Muslims...but since the Crusaders killed a lot of Jews too that name may be problematic.
I don't think anyone will use John again soon out of respect for John XXIII. I definitely would not expect any pope to pick Peter as a name.