I did both WAM, a regular REU, and RIPS. WAM I would consider to be something to do in addition to an REU/other summer research experience since when I did it, it was more of sitting in seminars learning about a topic, and then working on problems together with other attendees. It doesn't have the same research focus as the other programs, but it is still a really great program to attend. WAM tends to have more pure mathematics topics than applied mathematics topics, but they are fairly open in what the next few years programs are. It's also nice because it has both graduate students and undergraduate students. As an undergrad from a SLAC, I learned a lot about graduate school and coursework that I wouldn't have necessarily gained from the conversations that I had with my classmates. Also the food is A+ (or was when I went many years ago).
RIPS is also fantastic. I really liked that I was working at the interface of research and industry, and I got to go to a country I had never been to before as part of the experience. When we presented our research at the JMM, people who worked in the same industry were interested in the work we had done, so it felt nice that the research had real consequences. Of course, this is more for applied mathematicians than pure mathematicians. I also personally believe that RIPS looks fantastic on applications for applied math graduate schools. I also did RIPS after my senior year in college, and I liked that I was able to do another research experience before I applied to graduate programs.
There is also the Summer@ICERM (https://icerm.brown.edu/summerug/
) program that is run by the research institute in Providence, RI.