Asia Miles has gone through a lot of devaluations over the years and has very few Sweetspots left that can be booked with reasonable taxes.
Book British Airways Business or First Class from the U.S. to London with 70% fewer taxes
A well-known redemption that lets you book British Airways flights from the U.S. to London (https://awardcracker.com/how-to-pay-70-fewer-award-taxes-on-british-airways-us-to-london-flights/) remains unaffected despite the recent devaluation of Asia Miles for its own metal.
The above redemption with HKD 1811 ($230 USD) taxes works for flights departing from several U.S. cities (JFK, ATL, MIA and ORD), but for some reason the taxes are higher (HKD 3068 or USD 380) for flights leaving from DFW.
Book JAL Business Class 360 days ahead from the U.S. to Tokyo with reasonable taxes
There are other cheaper ways to book JAL business class flights (e.g., AA for 80K and Alaska Mileage program for 60K), but none of them let you book these flights 360 days ahead of time. Asia Miles are also easier to transfer from Amex MR and Citi TY points which makes this award redemption a lot more attractive. The total tax/carrier surcharges for this booking are reasonable around $250USD.
You can extend the trip to visit other cities in Japan for the same amount of miles (see the example below for two passengers).
Book JAL Business Class 360 days ahead from Tokyo to Helsinki or London with reasonable taxes
This is another great Sweetspot for the Asia Miles Program and can be used to extend your trip from the U.S. to Japan further to Europe.
U.S. to Madrid Roundtrip in Iberia Business Class for 126,000 Asia Miles and lower taxes
Iberia flight bookings with Asia Miles require roundtrip redemption and will cost only ~USD90 in taxes/fees for the entire trip. Booking the same flights with Iberia Avios can be cheaper (34-60K) based on the cities you are traveling from and the seasonality (https://awardcracker.com/master-your-avios-redemption-skills/), but the taxes are higher.
Summary
While Asia Miles are predominantly used to booking British Airways transatlantic flights to save on taxes, I like to use them to book JAL flights 360 days ahead of time, which comes in handy to plan your trip perfectly (e.g., leave on a Friday and return on a Sunday).