chilling wort with a partial boil

Just finished getting my first LME kits into primary.
My instructions tell me to cool the wort after boiling by immersing in ice water or using an actual wort cooler.
But I'm doing a partial boil, and diluting 2.5 gal. Does it not make more sense to cool the wort primarily during the dilution stage?
Thanks!

Sure, that's acceptable. Just so long as you don't pitch your yeast in hot wort, and you achieve a good cold break, whatever method you use should be fine.

I do partial boils as well and I usually chill mine in a sink full of cold water until it gets down into the 80F range and then chill it the rest of the way down with bottled water that's been in the fridge. It works well, but I don't think you're going to get it down to pitching temp with cold water alone.

To chill in the sink, just put the stopper in, set your kettle in there and fill the sink up with cold water. Don't go much past the height of the wort in your kettle though or it'll start to float and could tip. Stir the wort now and then as well as the water in the sink (different spoons of course) and it'll cool much faster. You'll have to change out the water several times as it'll warm up quick. The first time you fill the sink, it'll probably be hot and need to be changed by the time you get it filled. A second set of hands are useful so you can lift up the kettle while someone else reaches under and pulls the plug on the drain.

As ChshreCat said, you probably won't cool it down to pitching temp with just adding in the extra water. I wouldn't risk doing it that way.

What I do is boil my extra water (to make sure its good water) as the first thing before brewing and I just let it sit out until it cools down some then you can put it in the fridge or just let it sit out with a lit on it.

Then when I need to chill my wort, I fill up the laundry room tub with about 1/2 the tallness of my brew pot. Then I add 4 gallon size zip lock bags of ice (I just freeze 4 gallons a few days before I know I'm going to brew). Then you just leave the lid off and stir slowly here and there, and also move the water around. I get it to cool down under 80 in about 20-25 minutes doing this. Then I know its safe to add to my other water which is cooler.

That method has worked good for me so far, hope it helps!

what i did on my first two batches was the water that I was adding I put in the freezer until it was just about frozen and added that to the wort and it brought the temp down to about 80 deg. and by the time i sloshed it back and forth to add oxygen to it it was about 75 deg.

The thing with adding cold water when it's hot is that even if you get it down to 80 degrees or so, you have MUCH more mass you have to get down the last 20 degrees. It's easier to get a smaller amount of hot liquid cooled most of the way down, and then chill it the rest of the way with the top up water.