Mecca (or Makkah as pronounced in Arabic) is a region in Saudi Arabia, one of its cities is Mecca (clearly, the same name as the region's name). Other cities include Jeddah and Taif, which anyone can visit.
So, if you mean the city, then the answer is mostly No, if you mean the region, then the answer is Yes.
Going back to the city, according to Islam (as some interpret it), only the sacred area (the mosque area and the surroundings, other sacred areas like Arafah And Mina, etc.) is not allowed for non-Muslims. However, that is quite hard to apply due to Mecca being in the mountains area, so the ban is extended to cover almost all Mecca (it's not a large city anyway). There are road signs that show the Muslims-Only areas.
The photo is from Google. (Here is a link to one version on internet.)