As others have said, 1000 years is not a long time. There are plenty of structures on earth now that are over 1000 years old and many of them will likely last another 1000 years or more.
If we were exploring an alien planet and wanted to find out if any technological civilization had lived there then find ice and take core samples.
The pollutants, like carbon products from the industrial revolution to radioactive elements from nuclear tests would give you a good indication of the level of technology achieved.
Just as a side note, many civilizations in the past believed that they were living in the "end times" as some groups do now. But the average "species lifetime" (emergence to extinction) for mammals is around 1 million years, with some species of mammals lasting to around 10 million years.
Since modern humans has only been around for 200K years so far, we're really only in the first 20% of our history, and if we make 10 million years, we're in the first 2% of our species history. Either way, we are only at the start of human history.
Yes, cities, countries, political systems, and civilization may fall but we have plenty of time to start over and maybe do it better the second time.
