"The good season"? That's going to be spring. They don't flower in other seasons.
I know you're likely hoping for an accurate week or three, but much like the cherry blossoms, it differs from city to city, and from year to year (a warmer year = earlier than normal).
However, you can probably use the estimates of the cherry blossoms to predict the azaleas. The Bloom of Cherry Blossoms for example, does a prediction, and is currently forecasting blooms to start on April 3, with full bloom about a week later on April 9.
So based on that, April seems like a good time.
Scrolling down, you can see the past ten years of history for the blooms, and it's fairly consistent that the second week of April will either see full or first blooms.
Obviously, azaleas aren't cherries, but searching elsewhere seems to indicate they regularly bloom together, so it's a fair bet.
Bonus answer: a photo taken in Sendai in May, of an azalea in full bloom. However we can't know if it's in a garden, was at a florist or what, but it's an indication that bloom may go for a while.