There are several ways to research a question like this, in addition to asking strangers on the internet or buttonholing random students on campus.
You can look at the National Center for Education Statistics College Navigator profile of a college, and see how many people in last year's class had a primary major in what. You can usually also get that information, in more refined but less standardized form, from the websites of the registrars at individual universities, but that's more work. If you do that, you'll see that some of the most popular majors at Chicago are Economics, Biology, Political Science, History, English, and Mathematics. At a college that offers dozens of majors, those six represent about 60% of each class.
You can also look at different graduate program rankings at places like USNWR and phd.org. There can be lots of debate about the relevance of graduate program rankings to undergraduate majors, but I think they are pretty important. They tell you how strong the faculty's reputation is, and they tell you how attractive the department is to top grad student prospects, which translates into TA quality and interesting people to be around. Anyway, if you do that, you'll see that in addition to the majors listed above, it is very strong in almost all the social sciences, Physics and Chemistry, Art History, German and Eastern European literature and culture, Music History, and anything having to do with the Ancient Near East.
You can also look at what special resources and unique programs a university has. Those may not always be the best majors, but it usually means good faculty are attached to them. In Chicago's case, you might notice its Oriental Institute involving anthropology and archaeology of the Middle East, its involvement in managing the Argonne and Fermi National Laboratories (physics), the National Opinion Research Center (lots of cross-economics/sociology/psychology/statistics stuff), the Fundamentals major, top--ranked Business, Law, Medical, and Public Policy Schools, and the Committee on Social Thought. Among others.
My S1 is a third year at U Chicago. Oh, my - how time flies!!!!!
Originally he chose U Chicago for the economics department. He is deliriously happy at U Chicago. Over the years, what he found was what amazing quality of education he is getting at U Chicago overall in all of his pursuits.
By now I believe, at the level U Chicago is operating on (a tippy top school), it really does not matter what major you are picking. Unless you are choosing engineering, that is (ha, ha)!!!
I highly doubt anybody will be disadvantaged when applying to top tier graduate school program anywhere because Chicago was not ranked within top 5 in the area s/he picked was interested. Ditto with the job prospect: I don't think any employer will discriminate a U Chicago graduate because s/he majored in an area in which U Chicago is not within top 5.
Unlike Ph.D. programs, undergraduate educational quality is not so heavily dependent on the strength of the department of the major alone. After all, core requirement alone is quite a hefty portion of the total credits needed to graduate.
U Chicago is not for everyone. However, whatever difference in terms of the strength of the major is a minor issue in my mind, and should not be the reason to dismiss U Chicago.
Law, Letters and Society is a really interesting major. It's directed by Dennis Hutchinson, the editor of the UChicago Law Review (and quite a formidable, fascinating character), and takes 25 students into the program in their second year. You learn about law from a philosophical, theoretical perspective, and can take classes in economics, anthropology, history, political science and human rights to count towards fulfilling your requirements.
I really love the school, campus, city, and atmosphere at UChicago. But are there any majors or departments that they are known as being top notch for?
There are so many! Department of economics (i.e. Chicago School of Economics), department of physics, department of ecology and evolution, department of sociology (i.e. Chicago School of Sociology - UChicago was the first school to offer a sociology major and it was the birthplace of sociology), department of mathematics, department of statistics, department of genetics, department of psychology, department of public policy, department of art history and all of the foreign language departments.
A note on the engineering: UChicago fails to offer engineering not because it is a liberal arts school (which isn't entirely accurate in and of itself -- after all, the college has excellent programs and research in the natural sciences), but because offering an undergraduate engineering major would be impossible to achieve without reducing the number of Core courses. (Columbia is able to offer engineering by giving its engineering students an abridged version of their core curriculum, something Chicago likely won't do.)
On that note, UChicago's molecular engineering program will be a graduate program, naturally.