So, for some nice non-flavored black teas…
You could go with Adagio’s black samplers - they make a variety of samplers. There’s the Raja Sampler ($10) or the Silk Road Sampler ($15); those are both pretty standard black tea sets. There’s also an $18 sampler set, but I haven’t tried that one and reviews don’t seem as good on it overall. Raja has Irish Breakfast, Assam Melody, Ceylon Sonata, and Darjeeling Sungma Summer (I really like the Sungma Summer, personally, especially iced), while the Silk Road has English Breakfast, Yunnan Noir, Yunnan Jig, and Pu Erh Poe. I haven’t tried Silk Road, but pu erh teas in general have a bit more of an earthy flavor to them. Also, although the Rory Williams Pond fandom blend has sweet potato in it, it really actually brews up as a very nice breakfast tea, much more like a standard black than a flavored tea. Here’s the main black tea link for Adagio; of anything I’ve tried on that page, mambo is the only one I don’t recommend.
Most of the best Earl Greys from Adagio are actually Earl Grey blends with fruity additions, so I suppose I’ll pass on reccing any of those (River Tam is an Earl Grey rose that’s delicious but idk if rose counts as a flavoring - probably yes, so idk if your sister would like it.) Adagio will offer free shipping if you spend over $49 (which would be quite a bit of tea) but they do have a free shipping deal on any order going through Monday for Cyber Monday if you want to buy stuff fast.
For non-Adagio, I know Tranquilitea is a local shop that will ship places (site states it’s about $5 for nearby states to $8.50 if you’re on the West Coast and ordering 2 lbs or less; I’ve no idea about international shipping) - but they do have one of my absolute favorite black teas ever, Organic French Breakfast. It’s $4.25/ounce plus whatever it would cost to ship, with one ounce making about 10-15 cups of tea. They also have some other plain blacks that are nice: Imperial Breakfast is a very good, strong black tea that’s plain and about the same price range as the organic French. (But organic French breakfast, idk how much it would be to ship but I had to recommend it - it’s fantastic.) Their Earl Grey Creme de la Creme is about $3.50/ounce and a creamy but fairly standard Earl Grey. But they do have quite a bit of unique tea, the owners are fantastic about making recommendations, and zomg the Organic French Breakfast this is one of the very few teas I’ve ever bought 16 oz of. Also, if you want to buy her cheap tins, their shop has the best, cheapest tins of pretty much anywhere (I priced tins out extensively at all 3 sites and also at places like IKEA, Bed Bath and Beyond, and anywhere I could find things that looked like they’d work; they have metal tins for $3.99 that hold around 4 oz., although of course it depends on the volume of the tea as well as the weight - probably holds a bit more black tea than that.) This one’s a family-owned/small business.
The third major tea site I know of is Teavana. They’re super-expensive and mostly flavored teas, but their Golden Monkey is a pretty good standard blend, and I would definitely recommend the Yunnan Golden Pu-Erh if you want to give her an interesting black tea. The pu erh teas are rather smoky (but not smoky like a barbeque, like lapsang souchong - less smoky than that, more earthy and interesting, they make for fantastic iced tea.) The Yunnan Golden Pu Erh is $8/oz with a minimum 2 oz. purchase (like I said, Teavana is super-duper-ridiculously-expensive) but their pu erh is miles better than Adagio’s. (For non pu-erh plain black tea I’d probably stick with Adagio or Tranquilitea, tbh - Teavana’s strengths are in that pu erh black, spicy chai blends, and in some of their individual/unique flavors.)
(Also, if she considers oolong or white tea to be “real tea,” I would have some suggestions for those, but if she doesn’t usually drink white tea she’d probably find white to be too weak. Besides, you probably have enough recs to get started with here.)