The hotels are run by Loews and they have some type of Loews first card. Not sure if it is good at the HRH. AAA will also give you room discounts and a 10% discount at most restaurant/food carts/shops and a good discount on tickets.
PBH and RPH has the Loews card that you can sign up for on their website. The benefits are not great unless you stay often. Upgrade to next level of membership happens with multiple trips, not multiple nights. The lower level can get you a few things like free internet and late check-out. Higher levels get you some really nice benefits. Again, it depends on how often you can stay in these hotels, not the number of nights. https://www.loewshotels.com/en/YouFirst/Benefits.aspx
HRH has I believe the free All Access card. I have not stayed there since it stopped being a Loews hotel, so I don't know the exact benefits. We do however have an All Access paid card, but I think they now also have a free membership for the hotel benefits. I am sure the HR website will have the info. Someone can correct me if I am wrong.
The two Loews hotels also have some affiliation with American Express. You get points for staying. Since we don't have American Express, I really can't tell you anything more about it.