As others are saying, I think colleges which are welcoming to a wide variety of political viewpoints and have a strong norm of civil debate are fairly common. Secular (or all but secular) colleges which actually have anything close to the same sort of proportions as the general US public are extremely uncommon. The basic issue is kinda obvious–that age/education combination just skews way less conservative than the general public, so you’d really have to make a special effort in admissions not to end up that way.
As an alternative, I might suggest looking for colleges which fit the welcoming/civil requirement, and then are big enough that even a somewhat small fraction of conservative students still ends up as a decent-sized community.
Like, I think colleges like Chicago or WUSTL immediately stand out as colleges where there is fantastic Gothic architecture, great proximity to a major city, the norms of civil discourse are relatively strong, and there are enough students overall that there is going to be a decent-sized community of conservative students.
Someone else mentioned BC, and while I agree it is really not much different from its secular peers in terms of student mix, I think it would also fit into this general category. Similarly, someone else mentioned Fordham, and same deal I would think (the Rose Hill campus is really nice). Sticking on the Jesuit theme, Loyola Maryland has a pretty nice campus, just outside Baltimore.
A little less right in big cities, Indiana has a great campus, and Indianapolis is only about 1 hour away. Someone else mentioned Lehigh, which has a really cool campus, about 1.5 hours from Philly without bad traffic, actually not much longer to NYC (same qualification).
Finally, I would note Richmond is not necessarily a huge city, but it is decent-sized and a state capital, and under 2 hours from DC (absent traffic). Someone else mentioned the University of Richmond, and while it is smaller, it has a very nice Gothic campus, and is more businessy/pre-professional than most LACs. So I think if Sewanee might work for you, Richmond could too. Also mentioned was Rhodes (Memphis), and I agree that might work as well.