You book on AA in AAdvantage / Redeem MIles / Non-Air Mileage Redemption.
I was looking at Cat-5 hotel in Europe, 35K HH points/day, that will cost abt $150/day (Adv Purchase). But I can get it for 7K-9K AA miles per day (I think my target dates are too far now, dates 4-5 weeks out are 7K miles per day).
Part of it is that as an AA Plat I get 20% discount on the miles.