Summary: This is crazy powerful versus Divination Magic, plus potentially inconvenient
It's not quite clear to me from the question alone how all divination spells would be affected. Let's journey to the answer.
As Medix's answer indicates, clearly Mind Spike is a no. The target is you and Nondetection prevents you from being targeted. Done and done.
But area effects are less clear. If you are a fiend, does Detect Evil and Good target you? It does not, the target is Self with a range of 30 feet. To me this feels like the difference in direct attacks and AOE's for things like the Ioun Stone of Absorption
While this pale lavender ellipsoid orbits your head, you can use your
reaction to cancel a spell of 4th level or lower cast by a creature
you can see and targeting only you.
But the description is very specific. The Staff of the Magi is similarly specific about which spells it can absorb. Our Nondetection description is more vague.
So let's look at the full text of the spell:
For the duration, you hide a target that you touch from divination magic. The target can be a willing creature or a place or an object no larger than 10 feet in any dimension. The target can't be targeted by any divination magic or perceived through magical scrying sensors. [Emphasis mine]
Now it's doing more than the quoted text in the question. We are hiding the target from divination magic, not just keeping it from being targeted by divination spells. Now it's easier to say that the target is hidden from our divination Detect Evil and Good spell that isn't specifically targeting it. It's also clear the target will be safe from detection from:
- Detect Poison and Disease
- Detect Magic
- Arcane Eye
- Detect Thoughts
- Locate Animals or Plants
- See invisibility
There are some that might need DM decisions, but really all of these seem like they would fail:
- Beast Sense (doesn't really target the beast, but if the beast were hidden from divination I don't think it would work)
- Rary's (no talking to the mind of a nondetectable person)
- Foresight (I don't think you will be able to see into the future of a creature hidden from Divination), plus if the target of Foresight is the target of Nondetection the whole spell fails, and you've learned a valuable lesson about blowing 9th level spell slots via hiding from Divination magic.
Anyway, I just want to add, since I'm looking at spells, that there are some spells that aren't going to work while the caster/friendly target is under Nondetection, so beware:
- Comprehend languages
- Detect Evil and Good
- Speak with Animals
- Fortune's Favor
- Gift of Alacrity
- Divination, Contact other Plane, Commune, Commune with Nature (Range is Self)
- Foresight (see above)
One last area: Diviners. Subclass eatures aren't spells, they're definitely magical, and Nondetection works against Divination Magic, not just divination spells. Thus I would rule that a Diviner couldn't use a portent against a "Nondetected" creature, nor could the Diviner use one on themselves if they were Nondetected. Third eye is right out as well.