What stores can I find good looking, casual preppy apparel that won't cost me over a thousand dollars or more?
You might be able to find a secondhand one from APC on Grailed or eBay.
This blog post has some brands that make breton knits: http://putthison.com/post/4928849973/the-five-days-of-summer-series-part-i-bretons
American Apparel and H&M also have similar sweaters for $50 or so but they won't be too good. The latter is really thin and bad and I wouldn't recommend it though. IDK about American Apparel though