Having had a very similar camera (the slightly older D3300), two lenses I would personally avoid, due to disappointing experiences with both, would be the 35mm f1.8 DX version, and the 50mm f1.4G. I had two of the 35mm lens, and one was terrible, the other was just poor. Pictures weren't sharp enough for my liking. The same with the 50mm f1.4G; it isn't very sharp with the aperture fully open, and not really acceptable (to me) until you stop down to f4 or so. Which makes spending all the extra money a complete waste of time really. The 50mm f1.8G version is, by all accounts, and better lens. And a lot cheaper.
For your budget,
the Nikon 60mm f2.8 Micro might be a really nice surprise for your partner. It is a 'macro' type lens, meaning it can focus much closer than most other lenses, and you can achieve a 1:1 or 'life size' reproduction with it. Great for flowers/plants, insects, small details etc. Opens up a whole new word of viewing things. Plus, it's also great for portraits; it's not a 'portrait' lens, but it's very sharp, and the f2.8 aperture is sufficient to blur the background enough to make a subject 'stand out', particularly on full face shots.
Whilst others are suggesting 'faster' portrait lenses, such as the 50 and 85mm lenses, for someone learning, lenses with such large apertures, whilst desirable, are trickier to use. The large aperture means you have very
little depth of field, and a smaller aperture such as f2.8 will actually be preferable, to get more DoF and sharpness; with say f1.4 or 1.8, if the subject isn't exactly square on to the camera, one eye can be in sharp focus, but the other, not. Plus noses and ears can be out of focus. So the 60mm Micro lens might actually be easier to use, and get consistently better results. It's definitely a more 'fun' lens, in my opinion.
Beyond that; a longer 'telephoto' zoom would be nice; you can still take excellent portraits with it, and the extra 'reach' makes getting 'closer' to the subject easier.