Top CS PhD programs, do I stand a chance? I'm an American EE/CompE undergrad at a mid tier(top 200) smaller state school with a 3.96 GPA. I am the first person in my family to attend college, so you can imagine that getting advice on grad schools would be pretty difficult.

My university is not very big on research, so I have looked elsewhere for research opportunities and completed an EE REU at a top 20 university and a CompE Summer Research Program at a top 10 university. I'm looking to work on the Robotics/Perception/AI side of CS. I have posters and have given presentations on my summer research, but I don't have any publications. Realistically, what is my chance of getting into places like MIT EECS, Stanford CS, or UIUC CS? Is it even possible? Would they consider someone with my background, or is just a waste of money to apply?

I also plan on applying for fellowships such as NSF GRFP and will mention that on my application. I'm gonna be graduating in December, so I am currently applying for a prestigious CS research internship at a national lab for the spring(Jan - June). Assuming that I get accepted, would you list it on your Resume/CV in your application as a "future accepted position"? Or would that look unprofessional since you didn't start yet?

Am I at a disadvantage in terms of being a domestic student since most applicants are international? What kind of GRE scores should I be aiming for(I know some universities don't require the GRE)?

Thank you so much! I would really appreciate any feedback or advice that you may have. Sorry if my post is too long.
Let me offer some concrete data to support Buffy's answer, as a faculty member at one of the departments you mention (although I don't work in AI).  Short version: Your profile is definitely strong enough to be considered at Illinois, but your chances are low, because everyone's chances are low.

The computer science PhD program at Illinois received about 1100 applications for Fall 2019 admission.  More than 300 applicants listed artificial intelligence as their primary research interest.  (Another 450 applicants listed AI as one of their secondary research interests.)  We offered admission to 35 of these 300+ applicants; about half of those 35 accepted our offers. 

(I'm sure the application numbers are significantly higher, and the acceptance rates comparably lower, at MIT and Stanford.)

Almost all of those 35 admitted applicants were from universities with highly-ranked graduate programs.  A significant fraction of the accepted applicants already have research publications (or at least strong submissions) at top conferences.  A slightly smaller fraction are finishing masters degrees or applied to transfer from another lower-ranked PhD program.  (Every successful applicant with some grad school under their belt has already published.)

The main thing we look for in PhD applications is compelling evidence of research potential.  This evidence must be explicit in your CV, in your statement, in your choice of references, and in the content of your reference letters.  (Not surprisingly, this is also what the NSF GRFP and similar fellowships look for!)  So your application really needs to include strong letters from your mentors at both of your REUs.

On the other hand, the biggest resource constraint is faculty attention.  We only admit PhD applicants that get several positive reviews from faculty, and at least one faculty member declaring their willingness to advise.  Admission in AI isn't ridiculously tight because we don't want to admit people, or because we think the people we reject wouldn't thrive, or even because there isn't enough money.  It's tight because students require care and feeding, and AI faculty need to sleep occasionally.  So thinking strategically, you may fare better aiming at newer faculty, or at subfields where the department is growing.  (Hint: Robotics.)

Finally, if you're not accepted to a strong PhD program straightaway, you might consider joining a research master's program first, to build up your research track-record, and then applying again.  But then you really need to publish during your MS program to have a shot; PhD applicants with prior graduate-school experience are held to higher standards.  (Not surprisingly, this is true for the NSF GRFP and similar fellowships!)


  Assuming that I get accepted, would you list it on your Resume/CV in your application as a "future accepted position"?


Yes, absolutely!  (See: evidence of research potential.)  But be sure to describe the position in more detail in your statement, to remove any ambiguity.


  Am I at a disadvantage in terms of being a domestic student since most applicants are international?


No, not at all.  It's true that most applicants are international, but the average international applicant is weaker than the average domestic applicant.  (It's really hard to entice our own best undergrads away from six-figure salaries at Appflix or Twitbook or Ubazon or whatever.)  Roughly half of our PhD admission offers went to domestic students this year.


  What kind of GRE scores should I be aiming for (I know some universities don't require the GRE)?


MIT and Illinois don't require GRE scores (because we think they're useless as evidence of research potential), but Stanford does.  You should aim for the best GRE scores you can get.