You can’t apply to both Princeton and Harvard (which are both private institutions) early action as both exclude you from applying to other private institutions - you may only apply to other public colleges.
Early Action applicants apply by the November 1 deadline and hear from us by mid-December. If you apply to Harvard under our Early Action program, you may also apply at the same time to any public college/university or to foreign universities but you are restricted from applying to other private universities’ Early Action and Early Decision programs. You may apply under our Regular Decision program until January 1.
https://college.harvard.edu/admissions/apply
If you apply single-choice early action, also known as restrictive early action, on Nov. 1, you may not apply to an early program at any other private college or university. https://admission.princeton.edu/how-apply/application-dates-deadlines/single-choice-early-action
From a purely numbers perspective your odds increase more when applying early to Harvard (increase of 11 percentage points) than Princeton (increase of 8.9 percentage points). Also note that Harvard ranks higher than Princeton for computer science (see ranking table below).
If you are keen on applying to Harvard or Princeton and early to another institution I would suggest applying to the University of Michigan (which I note is another college of interest on your list) as it is a public college and other early action non-binding.
An alternative is to apply to MIT and CalTech. Both offer non-binding early action options, so you may apply to both as well as the University of Michigan. From a ranking perspective MIT ranks higher for Computer Science than Harvard and Princeton. The top twenty US colleges for computer science according to US News are:
| US New Education rank - Best global colleges for computer science (US only) |
Subject score |
|
| Massachusetts Institute of Technology |
1 |
100 |
| Stanford University |
3 |
96 |
| University of Texas--Austin |
5 |
95.2 |
| Harvard University |
6 |
94.3 |
| University of California--Berkeley |
7 |
91.4 |
| Princeton University |
10 |
83.8 |
| University of Southern California |
13 |
82.5 |
| Georgia Institute of Technology |
16 |
81.3 |
| University of California--San Diego |
17 |
79.5 |
| Carnegie Mellon University |
24 |
77.1 |
| University of California--Los Angeles |
26 |
76 |
| University of Illinois--Urbana-Champaign |
36 |
71.2 |
| University of Maryland--College Park |
38 |
70.8 |
| Columbia University |
44 |
69.5 |
| University of California--Irvine |
46 |
69.1 |
| University of Michigan--Ann Arbor |
47 |
68.9 |
| University of Washington |
50 |
68.5 |
| California Institute of Technology |
51 |
68.3 |
| Cornell University |
55 |
67.1 |
Apart from the information I have provided, the most importance piece of advice I can provide is that you should apply early to the college you have you heart on attending. Good luck!