There are a lot of misconceptions about “Applied Mathematics”. For one thing, the field covers a continuum of research activity with varying degrees of emphasis on theoretical proofs. Many applied mathematicians (like me) prove theorems (just like pure math) for problems that initially had their origins in an another field. Others create and research sophisticated computational techniques. And so on. Also, there are folks in CS departments that base a lot of their research on what many would consider “pure math”. Furthermore, OR departments and Stats departments are usually separate, but also do what could be termed “applied math”.
Second misconception is that an applied math PhD degree is marketable in industry. This is only marginally so - it really depends on the subfield, and the kind of connections that the doctoral adviser and/or department has. And academia is flooded with math Ph.D.'s looking for tenure track positions.
Before you start looking at graduate programs, you need to ask yourself why you need a PhD. Have you done research as an undergrad? You will need some evidence of that if you want to get into a decent PhD program. Also, there is a lot of variability in PhD programs, and I would advise you to apply mostly to R1 institutions. Those will have the most percentage of faculty with an active research agenda in a variety of fields.
As the other posts have already outlined, you will need to look at the each program’s website to see their departmental research agendas. Also, look at the math departments of big flagships with well regarded math departments: UMD, UMN, Univ Wisc- Madison, Penn State, Rutgers - they all have lots of information on their websites.