How narrow or broad should I look for undergraduate research?
I suggest you greatly broaden your search.  There are common features to all research.  Perhaps even look at research projects and programs in adjacent areas, like combinatorial research in computer science.
Since you could easily wait until the following summer to get involved in a research project, you can write programs and professors (in the area, or where you might want to visit) and ask about what you might do to prepare for the projects that exists.  If you do not know computer programming, perhaps that is a gap needing a fill.
It would be good to be exposed to many areas of mathematics before you decide on what you focus upon in graduate school.  I was convinced I wanted to to algebra when I was an undergraduate, but then topology started to be appealing.  In graduate school I switched to analysis.  Now I mostly do applied math research related to physics.