I've been to Tacloban 3 times last year but don't know the Asai star, I stayed in Alejandros hotel last time which is ok. Rob is the expert on Layte on the site I'm sure he will respond with some suggestions on where to stay and visit.
If your budget can go to it and you like a bit of luxuary then I would reccomend one of the villas at the Layte Park although I've heard from Rob that the normal rooms are pretty bad.
Enjoy your trip
