I'm currently an undergrad studying computer science: bioinformatics and bio chemistry. In looking for PhD programs somewhat related to bioinformatics, I've seen quite a few biostatistics ones come up. My focus might be genome science with the computer science background being a plus (not sure yet, still figuring things out, lol), but as a biostatistician do you do anything with genome science as whole? I know, pretty vague overall, but I'm still trying to find where bioinformatics fits into the scientific community as it's a very interdisciplinary line of study.
I'm not quite sure what bioinformatics is exactly, but I did do a bit of work on genetics data during an internship at the CDC. From my point of view, biostatistics is not bioinformatics. Biostatisticians and statistics as a whole are a large field, but there are definitely some people that intersect with the informatics realm. It's definitely not an area everyone works in though. If you're interested in genetics, and looking at biostatistics programs. I highly recommend Columbia's biostatistics PhD program. I interviewed there, and they had a very large focus on developing methodology for analyzing genetic data. I ended up choosing another program because I wasn't particularly interested in that area and I wanted to do a pure statistics PhD. However, it seems like you'd like it quite a bit.