Do you have any tips for students interested in 2 or 3 areas in the same department but not in the same area? For example, I'm in computer science phd admit in the USA interested in both cryptography and natural language processing. I need to choose now which area to pursue, so it's difficult for me to make a decision. Any tips?
Pick an advisor you like to work with, and work in whichever of those two areas that advisor works.
In general I think interest in broad fields is overrated, you'll be able to find problems that interest you in most fields. If you like it well enough to be considering the field then you'll certainly like it well enough to find problems that appeal to you. The only other factor I'd consider is whether one field is significantly better for industry job options, but since CS isn't my field I can't speak to that.
If you entered with a bachelors only, then you will have plenty of time to narrow it down. Your first task is likely to take the advanced coursework that will enable you to pass qualifying exams. You don't really need to pick a topic until you are done (or nearly done) with that task. Look at a lot of faculty as potential advisors and choose on more than just a narrow area. For example, the helpfulness of various potential advisors.
You might also be able to take a course in each area and perhaps with those advisors.
If you enter with a masters it is much harder as the time is shorter, but take some time to look around first.
You can always change your research focus later if you are able to obtain permanent employment. Your dissertation need not determine your life.