Jerry,
Without a doubt Ashford Castle, if you would like a lifetime memory of staying in a very top-notch castle that also (now) happens to be one of the top hotels in the world.
Almost five years ago, we stayed two nights at Ashford and two nights at Dromoland Castle. Both are nice, but Ashford is just more castle-like. If your budget allows both, by all means enjoy both. The walled garden at Dromoland is totally delightful.
Adare Manor is also a lovely place. We did not stay there (just stopped in for coffee), but it is more of a manor house vs. a castle.
The Hawk Walk rates as one of our top 10 travel experiences ever, and we have been blessed to have many travels and many experiences.
I'd suggest Googling: Hawk Walk, Ashford Castle or Hawk Walk, School of Falconry at Ashford, so you can view some of the videos of people enjoying the experience. Each person gets his own hawk, and the guide gives an introduction to hawks, along with instruction on how to launch/land them, and then you go out on your walk in very small groups (2-3) with the guide. Fascinating experience. Dromoland also offers hawk walks, but I personally think the vast grounds of Ashford offer a better location for that activity.
We did not participate in a medieval banquet in any tourist castles, so I can't share any guidance on that. The castle in Bunratty promotes such an event, and the Bunratty Folk Park (which we did visit) is delightful and a good representation of what life would have been like for my grandmother when she was a young girl in Ireland (according to my Irish cousin). We did visit the castle at Bunratty, and while likely more authentic (not redone for modern times), it was not nearly as grand as Ashford or Dromoland, but definitely worth the time to tour it.
If you make the splurge to stay at Ashford, I would recommend a deluxe room overlooking the front bridge and lake on the side. The original estate rooms are even spectacular, but priced accordingly.
Enjoy your time in Ireland. We loved it.