What do you call a person who doesn't like/hates traveling?

Solution 1:

We can call that person a homebody.

Solution 2:

Well, not a single word, but:

stay-at-home person

Christian Living Seven Days a Week - Page 121 Jack Mcinturff - 2007

a traveler, then this will not work unless the traveler becomes a person that is perfectly content to stay home or travel less, or the stay-at-home person learns to enjoy traveling.