Having worked for many years in both hotels and a central reservations office (which is where customer service was located for that chain), I've always recommended to compliment down and complain up.

Compliments:
When you run across an employee that goes above and beyond at a good hotel and you want to recognize that person, go to the chain website. Your compliment will get logged with Corporate before being sent to the hotel. All chain hotels must meet certain standards in terms of guest feedback. Compliments (either for an individual or the entire hotel) are used in conjunction with complaints during this annual review.

It will take a day or two, but the compliment will make it to the hotel and then it will be passed along to the employee. Additionally, your customer relationship management (CRM) account with the chain will include a notion that you complimented the employee/hotel. Different hotel groups will use that fact in different ways...but, it will never be considered to be negative for you.

[Anecdote: In my first hotel job, one of our Telephone Operators won Employee-of-the-Year for the entire hotel group. That honor came with 2 weeks paid vacation and a 7-night almost-all-expenses paid trip for 2 to Aruba. One of the reasons he won was because he had multiple compliments that originated with the chain.]

Complaints:
If you have a complaint, it's usually best to start at the lowest reasonable level and work up. Basically, this is what liondragonx5y mentions. This strategy is best because you can continue to elevate the complaint to people with more power if you don't agree with the resolution (see caveat).

For a limited or extended stay brand (like Hyatt House), the Front Desk Managers tend to have good deal of influence within the hotel. As such, that person would be able to work with the Housekeeping and/or Maintenance Departments to address your concerns. (Larger properties with more employees might have more distinct chains-of-command that might require action from a Rooms Division Manager/Assistant General Manager/General Manager instead of a Front Desk Manager.)

Personally, I'd start with the Front Office Manager. Be sure to mention the fact that you are likely to return to the hotel. If you already have future reservations, slip that into the conversation.

Caveat: All hotel groups tend to operate under the philosophy that individual hotels are responsible for handing their own complaints. As such, appeals to the chain Customer Service Department or the hotel group Corporate Office usually won't change much. Those people will usually only overrule the hotel's response to a complaint if a policy was broken or if the case is egregious. (Questionable cleanliness or maintenance usually wouldn't rise to the level.)

TL;DL: Start your compliments using the hotel chain website. For complaints, start at the hotel so that you can appeal up, if necessary.