Don't know about AMS.
There's no Hilton property near BRU. Sheraton is right next to the airport, just across the street. All other airport hotels require a (mostly free) shuttle. Call the hotel and ask them if they can keep your luggage for a few days, I think chances are high they will not charge if you also book a room. Alternatively, BRU has got lockers (not very big) and provides a luggage service for oversize items (€7.5 for first 3 items). From the website, it's not clear if they keep it for over 24h. http://www.brusselsairport.be/en/pas...ggage_lockers/

Why anyone would like to trade Belgian beer for American is beyond me, but hey, good luck!