I don't have any easy answers to the "Micro first" vs "Macro first" debate when teaching Introduction to Economics. But this is what I do, and it seems to work a bit. And I have probably taught Intro about 30 times in my life. That experience should count for something.
1. We (Carleton University) are one of the last holdouts that refuses to split Intro Economics into two half courses. We are being "difficult". But I refuse to say someone has had an introduction to either micro or macro unless they have had an introduction to both. You need to be able to see it from both sides, or you can't really see it at all.
2. We start out with micro, BUT..........................
I start out with a Production Possibilities Frontier. Apples and Bananas.
You can teach a helluva lot with just a PPF. And not just opportunity costs. What is the relation between the slope of the PPF and the relative price of apples and bananas? Why is the PPF curved, and what does it mean? (And unless you can answer that question, you do not understand why supply curves slope up.) And what does it mean if the economy is inside the PPF?
Next I teach comparative advantage and trade. For that you need two PPFs, with different slopes. You can call them "Farmer" and "Rancher", or you can call them "Canada" and "US".
I first assume barter. The Canadian BIB students know they can make a profit by "buying low and selling high". So they fill their canoe with Canadian apples, cross Lake Ontario, swap their apples for US bananas at the US relative price, then paddle home, swap their bananas for apples at the Canadian relative price, and find out they have more apples than when they started (minus what they ate while paddling). Which is their Profit! So other traders follow them, so Canadian and US relative prices converge. Standard stuff.
Then I introduce Money, and The Nightmare Scenario. Cue scary music. What happens if the dollar price of both apples and bananas is lower in the US than in Canada? Will free trade with those dastardly clever cheap productive Americans cause mass unemployment in Canada???
Then I talk about exchange rates. Whose "dollar" are we talking about? Yes, if the exchange rate is too high, The Nightmare Scenario would indeed happen.
But we don't blame free trade for The Nightmare Scenario; we blame the Bank of Canada, for keeping the exchange rate too high. The Bank of Canada should print money, to make the exchange rate drop, until Canada can export apples.
The alternative, under fixed exchange rates, is to wait for mass unemployment to cause Canadian wages and prices to drop, until Canada can export apples. Which might take some time.
Then I go on to all the regular micro stuff, like demand and supply curves. (Because demand and supply don't make any sense unless you understand why people trade. Which is why Mankiw does trade theory before demand and supply.)
I'm not saying it works perfectly, but it seems to work. The students understand that if the Bank of Canada gets it wrong, the economy will be inside the PPF, and all that opportunity cost stuff might not work. And it only takes about 20 minutes extra to teach it, on top of the regular micro stuff. It's totally unrigourous of course, but so what.
It probably works better in a smallish open economy like Canada; I'm not sure how I would do it if I were teaching in the US.