If she liked
Sailor Moon, she'd probably also like
Magic Knight Rayearth.
No Need for Tenchi is good, based on the other titles you say she's read. I can ask my daughter for additional suggestions if you're interested in more manga-- it seems that they have fairly similar tastes. Sounds like you've got quite a nice collection for her already.
Unfortunately, I don't know of any legal ebook sources of these manga yet. There are those who are of the opinion that if you buy the originals in paper, it's reasonable to download ebook versions when they are available from other sources. This can save storage space, which can be relevant in a hospital setting, but whether you think it's appropriate or not is up to you. And storage space is less likely to be an issue at her grandmother's, I suppose.
If you're also picking up anime from netflix or wherever, "Vision of Escaflowne" would probably be a good choice for her, but don't bother with the manga version, which is nothing like the original anime. Conversely, I recommend
Revolutionary Girl Utena in manga form, but the anime version is more challenging to watch.
For the Pern books, I recommend starting with the "Harper Hall" trilogy:
Dragonsong,
Dragonsinger, and
Dragondrums. Not that there's anything wrong with the first books McCaffrey published (
Dragonflight and
Dragonquest), I just thought the Harper Hall books were better-- certainly they appealed more to me at that age. The later ones vary more widely in quality.
Ah. How could I have forgotten to mention Madeline L'Engle? Particularly
Meet the Austins,
The Moon by Night, and
A Ring of Endless Light, and probably also
A Heart like a Lotus. Less well known than her series starting with
A Wrinkle in Time, but probably will appeal to your niece.
Best wishes to your niece for a speedy recovery!