Even if your main interest is in paleoanthropology, I think it is still possible to do it without a lot of traveling-- outside of the US for long periods of time, at least, as you mentioned. Within physical anthropology, I think there are some people that are lab-based and other that are field-based; within paleo, some people are always the ones out finding fossils, but there are still others that don't necessarily go out to the field, but can still analyze fossils if they have the right connections, and/or do research on collections.
Some programs might encourage (possibly require) some type of field experience, and in general most researchers promote international collaborations, but if it's definitely not an option there are likely ways to fulfill these without traveling abroad (e.g., get field experience excavating Eocene deposits associated with early primate evolution in west Texas - or something like that, still within the US).
If fieldwork out of the country is not an option for you, I think there are still other options available. There would still be traveling associated with conferences/presentations, data collection (e.g., at museums, like the Smithsonian), and that sort of thing, but not necessarily regular international travel. Just my thoughts!