A trick is to know which brands you need. Marriott's Residence Inn is a big reliable one (for multiple "rooms" and kitchen/laundry) that exists almost everywhere in the US. It's a part of the whole Marriott system and often in tourism lulls in various cities has deals that keep it comparatively well priced with other Marriotts in that city and will let you use Marriott points to further defray costs.

Hilton and IHG both have similar brands, but their exact names escape me at the moments. The search keywords are "extended stay" and "apartment hotels".