Buildings or items that are falling apart or "shabby".
“The hot tub is under filled so there's not enough water in it for the catch filter to even get water. So the hot tub is filthy. It's filled with what looks like dissolved oatmeal that just floats on the surface of the water. It's absolutely disgusting.” Facebook · Campground Reviews · 8 months ago
When used as an adjective, "run-down" describes something dilapidated, neglected, or exhausted. In reviews, this is often used to criticize maintenance or quality.
“The rooms online do not look like the rooms they have guest staying in. Our rooms carper and couch was so dirty the stains were obvious. Staff were not really friendly but somewhat helpful . Just not a fun experience here.” Tripadvisor RUNDOWN Definition & Meaning - Merriam-Webster
A "rundown" is a quick report or item-by-item review that provides the main points of a topic or project. In a professional or creative context, it typically includes: What has been accomplished so far. Next Steps: What is planned for the immediate future. Key Issues: Any concerns or questions that need addressing.
“Upon entering it was immediately apparent it was a bit run down... 9/10 of the bars/restaurants were in fact closed. The casino had a few people milling about but not nearly enough to take even 5% of the space.” Tripadvisor