Lawrence is essentially suburban – Appleton is a city of ~80000 in the Fox River Valley, which has Green Bay (of Packer fame) at the northern end and Fond du Lac at the southern end. Oshkosh (of Oshkosh B’Gosh fame and a big annual EAA event) and Neenah are two of the other larger towns in the area. I think it essentially resembles a suburban sprawl, and Appleton is in the middle of it.
Beloit College is in a town of about 35000 45 minutes south of Madison and maybe 90 minutes from downtown Chicago.
Lawrence and Beloit are very close academic peers and are considered the top two LACs in Wisconsin.
Both are good schools, with their share of intellectualism, and would be low matches or safeties for the OP.
I believe Earlham is in a smaller town than Appleton or Beloit. Without looking at Maps i'm not sure about its proximity to cities. It is another fine option probably in low match territory.
I think we’ve already named many of the most intellectual urban or suburban universities and LACs. (and in the case of the LACs, if they are rural, they’re at least within 30-45 minutes of a large city).
If you include truly rural intellectual LACs, you’re adding many more quality options, like Williams, Hamilton and Middlebury. That’s up to you, OP.
Keeping Clark, NCF and Sarah Lawrence as safeties means you have three quality options, which (imo) should be plenty, provided you like them.
Finally – I think Brown is fairly intellectual for a university, but by reputation, at least, it is not hard like Columbia, Chicago, Carleton, Swat, or Reed. That said, with the open curriculum, I suppose a student could make it about as challenging or as easy as he or she wished. So if the OP ended up at Brown and wanted to fashion an academic gauntlet, she likely could. The overall academic intensity of the place might pale in comparison to some of the others, but she could make Brown as hard as Brown can be.