I'm not sure whether this piece of advice is generally useful or not, and it's almost certainly variable depending on field; but I do wish I had followed this when I was in graduate school.

Fairly early on, choose a thesis topic or problem you're interested in, and pursue it. Don't get side-tracked into something just because it's what the department or your advisor is working on. In fact, I'd go so far to say you should pick your thesis topic before you apply. Use that to help you decide where to apply. If you don't have a thesis topic you're committed to, you're not ready for grad school; and should stay out.

If you can swing it, get informal approval for your topic and an agreement from a faculty member to serve as your advisor before you apply. This is easier if you're attending grad school the same place where you're an undergraduate, but it can be done as long as you have some notable research chops as an undergraduate.