My 93 1.6L 16V Sidekick idles crazy fast at first start. Like
2200 RPMs. It idles down to about 800-900 RPM when warm

I've searched and found it could be some vacuum solenoid issue?

I noticed that on one it looks like something is broken off yet the
line diagram looks like all lines are good. The broken looking part
is on the top.

It's the blue one.

Should I plug the visible hole?

That is how the engine is supposed to operate.....high idle until the engine starts to warm up, then the idle gradually decreases as the engine warms up, until it settles down to 800ish at operating temp.
What is broke off the top of the solenoid is the filter.  Do not plug the hole.

I get that any car will have a higher idle at startup when cold.
But I've never had a car push 2200+ RPMs when cold. I am
concerned especially when it gets to sub zero and oil just doesn't
flow well.

And by cold, we're talking even at 70 degrees outside.

It can't be good for the engine to race from 0 to 2300 RPM with
little to no oil present.

Thanks

I get that any car will have a higher idle at startup when cold.
But I've never had a car push 2200+ RPMs when cold. I am
concerned especially when it gets to sub zero and oil just doesn't
flow well.

And by cold, we're talking even at 70 degrees outside.

It can't be good for the engine to race from 0 to 2300 RPM with
little to no oil present.

Thanks

Check the IAC valve.
Yeah, 2200 is a little high...I was thinking mine stayed closer to 1800.
Yep, 70* is still cold enough for it to go to cold idle speed.  It is more a coolant temp deal, instead of a air temp deal.  It can be 30* out, but if the coolant temp is up around 200*, then it won't rev to cold idle.

Post up a picture, your description of the broken part is rather vague sounding, also if it is a broken part it should be repaired/replaced and not disabled.

My 98' Sidekick as well as every other modern I4 engine I have owned and/or worked on, has a rather high idle when the coolant is below 140 degrees or so. The higher idle is far easier on engine wear than a low idle when the engine is in a no load condition. Though different platforms will have a slightly different cold start high idle, it is always in the 2K range, give or take a few hundred rpm's. This is part of the reason for the 5w oil requirement.

Post up a picture,

I tried with no luck...... I am technologically challenged

This is part of the reason for the 5w oil requirement.

Yikes!!! I think the oil change guy has been doing 10w-30w

Yikes!!! I think the oil change guy has been doing 10w-30w

I run 10w30 in my 1.6s and 5w30 in my 1.3s and have had no oil related issues with any of them.
10w30 is good for down to -4*F and up to 86*F.
5w30 is good for down to under -22*F and up to 50*F.

Skyhiranger , whatis the IAC valve ?

I slightly mis-spoke earlier when I stated the cold idle is 2K = or - a few hundred, it should have read 2K tops with most several hundred below that, sorry.

2200 is a tad high for a cold high idle. But as long as it corrects itself as it warms up, then I wouldnt worry too much.

I use the 5w30 during the winter and a 10w30 during the summer months only.

Skyhiranger , whatis the IAC valve ?

Idle air control valve.  It sits between the valve cover and the top part of the intake (it is actually bolted to the top part of the intake with 2 horizontal bolts).  It has 3 rubber coolant lines hooked to it and a blue connector.  To test it, just test the resistance of its internal coil.  If it is out of spec, it can make the idle incorrect.  But I doubt yours is bad.
Another issue they sometimes have is the internal parts of it get gummed up and stick or don't move as much as they should.  You can take it off and clean it out with brake cleaner or carb cleaner.  Again, I don't think that it sticking is a real common issue though.

I use the 5w30 during the winter and a 10w30 during the summer months only.

i think that is a good way to do it.  I probably should do it that way, but I don't.