Harvard Yale Georgetown Columbia Berkeley Stanford UPenn Duke Cornell are some that come to mind for me, but I think that this really depends on the person and to some extent on the region (I had a writing professor who is also a prosecutor who seemed to have hardly heard of Cornell, but I also know an attorney in this region who seemed to think extremely highly of Cornell).
I actually think Chicago tends to have a fair amount of lay prestige because it is generally reputed as one of the best universities in the country in academia IMO, but I can see why some wouldn't know of it as a great law school if they weren't familiar with the general academic prestige indexes of major universities.
Although I think of Stanford as extremely prestigious in general, for some reason I didn't think they had a law school until I started researching schools, and then once I saw they had a law school I don't think that I was aware that it was one of the very best. I don't know if this is generally true, but for some reason Stanford Law (on very first impression pre-law school or research) wouldn't have sounded as prestigious to me as it rightfully is.
I didn't realize what a great school Michigan is for some time, but I think ppl in academia, as well as many lay people, know what a strong rep it has. UVA I think has very low lay prestige, in part because the rest of the University isn't tip top like the law school as far as I know. I think Vanderbilt has pretty decent lay prestige, but until I looked into law schools I personally wouldn't have thought of it as a particularly strong school (it could have been a T2 as far as I would have know). UCLA I thought of as fairly prestigious, although that probably had to do with the region I was in partly. If anything. UCLA's lay prestige probably outweighed how highly I think of their law school now. NYU is a school that I think has relatively low lay prestige, especially compared to Columbia. I've known for a long time that NYU has some top science-related programs, but for some reason I still have a hard time getting my head around the fact that it is a top 6 law school. I'm not at all saying it shouldn't be, I'm just saying that in my mind it well outranks its lay prestige.
Does it matter? I think in certain contexts--such as business--it might, but mainly I think prestige in the legal community is more important, because this is where the recruiting is generated. I also think many sophisticated clients will have some idea of what law schools are the best, in spite of lay prestige.