I have booked the flight already because my flight to Bangkok is in the end of Songkran Festival period (It is a long holiday in Thailand and a lot of Thai people will come to Japan. They will go back to Thailand in the end of the period). If I did not book the flight, there would not be a seat for me. But I can change my arrival flight to 16 April without any fee.
Last time I went to Japan, My flight to Bangkok was on 28 October at 0:20. I walked though immigration on 27 October and the officer stamped "27 Oct" in my passport. So, I think that if I go through immigration on 16 April, my stay in Japan will be exactly 90 days. However, I will ask the Embassy of Japan in Thailand about this on Monday about this.
I saw in the website that there is also a bus service in Haneda airport which connects Haneda airport and Tsukuba station as well.
http://hnd-bus.com/route/tsukubacenter.html
I choose Haneda Airport because the flight time suits me, compared to Narita airport.