Tuesday Mornings and Burlington Coat Factory have some linens, tho I’ve mostly stuck with Ross–low prices and nice quality.
@conmama, I got my son Martha Stewart fast drying towels from Macy’s, and he used them for a year and they still look fine.
I second the recommendation for Company Store. That’s where I got my older son’s comforter and sheets.
In defense of your D, the comforter is one of the only ways to assert your style in a dorm room, so I partly get it. My D was picky too.
First year, D chose a duvet and cover from ikea. Third year, I made a duvet cover out of a sheet to use with the original duvet.
FWIT, I’m a big IKEA fan! 
My D likes the down (they also have a core loft) blanket (a little wider than comforter) from Garnet Hill. She has a throw from the same collection too!
If you can, hold off until into August, you will be amazed by how the dorm supplies multiply seemingly overnight!
She may like a cotton blanket or a quilt as a cover up instead.
A comforter with a duvet is more versatile and she can change the duvet later if she tires of the print. D, and a lot of girls at her school, went with white duvet covers, then added a colorful quilt. The combination works well for a wide range of temperatures. A regular twin comforter/duvet or quilt works fine on a twin XL bed. You really only need twin XL sheets.
My son took his comforter from home and left his bed at home with just the sheets and blanket. Do you really “need” a comforter on the home bed that won’t be used? Can’t it be neatly made with just sheets and blanket? When he came home for holidays and needed something warmer, he just used a really old comforter that we still had (it was actually light pink, so it wasn’t really very “boy” and put it back in the closet when he returned to school). He said he was manly enough to use a light pink comforter
My g/f ordered one for my son from LLBean. Years later, when his room was more on the aqua side, I found one at bloomies, 70% off. He got one at ikea, but never liked the flower design (he was there buying bed and dresser, so just bought). He keeps one in LR now. With all the moves, they don’t last more than a few years.
Now I’m getting way fair ads, so they probably carry comforters.
I have never met a duvet cover that stayed neatly “attached” to the comforter. And it is a hassle to put it on! Plus, I doubt a college student would remember to wash it. A $20 washable comforter from Target can be used, for a year or two, washed together with the sheets, and then the student can get a new one if the needs comes.
Make sure your kids LOVE duvet covers before you get them. Neither of my kids had any use for them. They were simply too hard to get back ON the duvet. My kids preferred plain old comforters.
Attachment can be an issue with a duvet. The duvet I bought D has corner ties inside to tie the ends of the comforter. I also attached a few double sided Velcro strips along the top and bottom edges of the comforter and duvet to keep everything in place. It has worked well for my D, but I can see where it might require too much effort for some kids (including my S who used a regular comforter). He would have been completed frustrated by a duvet. Lol.
My S didn’t even want to buy a comforter. He doesn’t like a lot of covers-he usually only uses a sheet, sometimes a blanket. So easy…
D got one at Ikea freshman year but never used it as the dorms were too warm all winter in a cold climate. She ended up donating it at the end of the school year.
We are currently using our duvet covers as curtains in D’s room. They are in great shape (as they were barely used) and keep out the light so her room remains dark (and cool), allowing her to sleep in as needed when she visits.
We initially thought they were great and bought quite a few of them. Our kids never warmed to them, tho D would sometimes use them as a blanket (especially the flannel one).
We don’t normally shop at K-Mart, but six years ago my D found her college dorm bed comforter there. She purchased nicer sheets (she likes the Pure Beech Jersey Knit Sheets at BB&B) but the thread count didn’t matter so much on the comforter. Plus it was so inexpensive (less than $20) that I didn’t care if it got ruined along the way. It actually wore well and made it the 4 years. So you might want to expand your search to stores you don’t normally shop at, like Sears, Burlington Coat Factory, Tuesday Morning, TJ Maxx, etc. We also recently purchased a duvet cover for our guest room from Overstock.com. I purchased the comforter that goes inside the duvet cover at Ikea.