How can a senior undergraduate find academic journals in math and computer science?
I would agree that you should mostly be ignoring journals and focusing on conferences, as they publish the majority of new computer science research.

Microsoft Academic Search is a good place to go to get an approximate listing of the top conferences for each sub-field of computer science. Other fields other than Computer Science are listed there too.

Use your school's network to access the ACM Digital Library (this should be free through your school's library), and download the proceedings for the conferences in the past year or two. Find the papers that look interesting to you and then search for them on Google Scholar. You can print them out if you prefer hard copies.

Hope this helps!