It's not an endorsement, but I've stayed at some hotels with "pure rooms" or allergy-friendly rooms. They supposedly go through periodic special cleanings and usually have a filter and allergy-friendly bedding. I like them, but have never had to pay extra, as most hotels I have status at are happy to offer it as an upgrade. The standard does vary, as I'm not sure what the upkeep is on a daily basis, but it's somewhere to start.

http://www.pureroom.com/

It seems they have a handy search that lets you price out specific nights for all the pure rooms around the city.