This is all just from my own previous application experience and what my undergrad advisor has told me, but I think what's ultimately important about a program is how well the department can support you, if it has the resources to fulfill your research goals, and if the professors there are knowledgeable in your intended research area and if they have contacts you can draw upon. Obviously name recognition probably plays a little (and being a bigger or more known school also ties into how much money the department may have to help fund you). To take UChicago Anthro department for example, they're well known for leaning more heavily theoretical (both in the cultural and archaeology side) and are also very hands off with graduate students (heard from a friend attending that grad students there can take 8-10 years to finish a Ph.D.) which might not be a good fit for some people-- it's still a very good department, but fit is important! (I am also not sure what rankings there are and it may be more personal perception by professors than any definitive list out there.)
Also I'm not sure what University of Illinois campus you've been admitted too, but from my brief experience at UIUC working in their labs for my own research project as an archaeology student, the Anth department seems pretty large and has a lot of well supplied lab spaces... so again, depends on what you're looking for!