Go through your results for flights to Aomori in Japan with Netflights. Although Japan Airlines usually has the best prices, it's best to double check what's available for your travel dates.
If these flights are too expensive, try searching for a different time of year. So if your dates are flexible, consider looking at different times of year.
Look out for flights with Japan Airlines, as they often have good deals. Or broaden your search by looking at other airports in Japan.
Looking at a few different departure airports will give you even more choice. See what you can find. And remember, it's best to book your flights in advance wherever possible.