Do I have a chance at competitive programs?

[nobonesaboutit]

I'm studying Anthro at a smallish, not extremely prestigious university.
I will be graduating in Fall with a 3.8 GPA and (hopefully) GRE scores within the 160s. 

I worked on an archaeological survey in Greece two years in a row, the second year I was a group leader. And this summer I will be doing a forensics field school.

I've won awards for public speaking and have presenting research at a symposium.

 

I'm looking at fancy programs like NYU and UC for physical anthropology with a focus in human origins and paleoarchaeology.

 

Are these reaches? I feel like they are...

And if they are, any suggestions on what a better fit for me would be?

[Tachiyaku]

I don't think they're reaches at all. The project you pitch and how you pitch it is way more important than your grades or the school you go to. However, this isn't to say that grad school admissions are a complete meritocracy, it's always a little bit of a crapshoot ultimately. Apply wherever you want to, and good luck

[hipposhippos]

You sound well positioned to argue that you are prepared for graduate work. What is most important is your ability to articulate a particular research question or questions. You'll need to be well-versed in your area of interest and have an idea of where you want to dive deep. This needs to match up with your qualifications and also appeal to faculty with similar interests. But you sound like you're well on your way to figuring these things out! Good luck!

[sarab]

It looks solid to me! Work on good statements and apply to programs that are a good fit (seems you have that figured out). Good luck!

[AKCarlton]

Agree with the others, you seem well-prepared to compete for a place in a good program...just make sure you apply to more than just your top choice...find the professor(s) that are willing to work with you and have similar research interests.