Either way is ok:
1) ABC is a company based in (both) Silicon Valley and Atlanta.
2) ABC is a Silicon Valley and Atlanta-based company.
However, because the company is based in more than one place, #1 sounds slightly more natural. If the company were only based in one place, then it would be just as natural to say, for example, ABC is a Silicon Valley- based company. But honestly #2 is fine too.