This is a card that has worked both better and worse than I expected, once I started trying it in actual decks!

My original thought was that, while it would be a potentially neat surprise, it would rarely actually fire, and would usually just be a form of click compression - sort of a mini Replicating Perfection, forcing the runner to go run Archives first, if they want to run your remote. (Or blow a Pinhole Threading on it.) It wouldn't actually do much to a cautious runner.

From playing with it though, I've come to realize that it actually has several forms. The first one you draw, actually needs to go straight onto archives, and doesn't do much to protect your agendas. (Aside from making it slightly safer to store them in archives.) And suddenly, archives is very scary to check, especially if they have to pay to break some ice on the way in.

But now that Archives is scary, a whole bunch of stuff gets better. Hybrid Release is more likely to have a target. Regenesis is more likely to have an agenda to pull out. And of course, the next two Nanisivik Grids you draw are much easier to keep active.

You only get to fire one subroutine, so you really want ice with flexible, impactful subs. A few of my personal favorites, in startup format:

• Ansel 1.0 is a little expensive on the influence, but is one of the most damaging things you can trigger. You can just trash any one runner card, so you can rigshoot programs, and even sink Endurance. (Which feels very nice when it happens!) Alternately, in a pinch you can use its last sub as a pseudo-end-the-run, to protect an agenda (and the grid itself!) if they can't afford to get in a second time that turn.
• Rototurret and Ballista are both good because they're flexible - you can use them to end runs if you need to keep the runner out, or trash a program if you are willing to let them trash the grid, in exchange for taking a bite out of their rig. Ballista is more expensive on the influence, but is also more taxing if you rez it like normal ice.
• Bathynomus is the biggest single hit of net-damage available. And it has the nice side benefit that it's a card that you probably want anyway, since it is a good way to discourage archive checks.

One other thing I've noticed is that if you're playing Nanisivik Grid, you probably want to include a little more ice than usual. Just so that you have enough to toss some into the bin without leaving your servers undefended. In fact, since you'll be tossing cards into archives more than usual, it makes sense to pair it with other cards that have synergy there. Happily, modern Jinteki has a lot of such cards! A few of my favorite pairings:

• Hansei Review is a nice, simple way to gain 5 and put a card in archives without having to overdraw/discard. Solid econ, and with a downside that is actually an upside here.
• Jinteki: Restoring Humanity is just a nice synergy, since it wants to have at least one facedown card in archives anyway. (And makes it hard for the runner to know if you're discarding just for the money, or because you're laying a trap.
• Hybrid Release and Regenesis both benefit from facedown cards, as well as the runner checking archives less frequently.
• Moon Pool is a great way to throw cards into your archives mid-run. There's a rez/activation window before the grid triggers, but after they've passed their last chance to jack out. So while it sucks using Moon Pool on something other than scoring an agenda, it can make for a really funny surprise if they think the grid can't hurt them! (And of course, you can use it to fast-advance agendas out too.)
• Hafrún and Anemone are both also ways to get ice into archives mid-run, although the runner can still jack out if they realize what's up.
• Simulation Reset lets you pull faceup ICE back into your deck, while dropping new, facedown cards into archives, which is pretty great.
• Kakurenbo isn't startup legal any more, but it can be an absolute game-changer. If you play it late when there is a lot of ice in archives, you can absolutely supercharge your Nanisiviks!

One final thought - while it's tempting to think of this as only a defensive upgrade, it's worth remembering that it can also make a very effective trap! You can just install it naked somewhere, and if the runner goes to check it, BAM, their boat sinks, or whatever. (Bonus points if you install it naked, protecting a Moon Pool, so if they run it, you sink their boat, but if they don't run it, you can just fast advance out a 4/2 at your leisure!

So yeah. This card does work! It fits in really nicely with all the other archives-based shenanigans that Jinteki has been getting lately, can be situationally very powerful. But it also feels like it has some counterplay, and requires some setup to be really scary. It's also a really interesting counterpoint to ZATO City Grid, which has a similar effect (forced subroutine firing) but has a very different cost/setup. Fun stuff!

This probably will see the most play in Jinteki as a fairly reliable way of getting high-value subroutines to fire. In Jinteki, the most dangerous target is Bathyonymous' 3 net damage. Secondarily you may see an end the run or maybe some wacky play around Aimor or Otoroshi. This card gets nuts on HB ice. Bloop and Fairchild 3.0 can inflict a brain damage, Tyr can inflict two brain damage or "trash a Runner card and gain $3".

I suspect this will see play in HB brain damage decks because paying $2 to reliably trigger a subroutine of an unrezzed ice is crazy value, and the card that creates this crazy value protects itself under its own forcefield of pain.

The most practical counterplay is probably Pinhole Threading or Caldera. If you can deal with uninteractive damage with Caldera, then Nani is just an (exhaustible) engine of end-the-run subroutines. Oh by the way Tyr also has a subroutine that can trash Caldera. Light the Fire theoretically could work, but probably will not. (Incurring a brain damage is a big cost against a deck trying to inflict brain damage, and at least one identity likely to use Nanisivik - Aginfusion - can bounce you out harmlessly on a LTF run).

I'm not sure a self-protecting card which can trigger a subroutine on an unrezzed ice is workable in the current card pool.

Update: Nanisivik is banned in Standard as of March 2023. "Banning Nanisivik Grid was a hard decision—it is very frequently an interesting card, but installing one on Archives makes it extremely difficult to trash without the use of specific tech cards." Banning Nanisivik makes it easier to delay runs on Archives. Having to run Archives to deactivate Jinteki cards like Nanisivik was not very fun. I think Regenesis is closer to a right track, the corp has to ante up an agenda in Archives to use Regenesis, so breaking up a Regenesis play is more rewarding.