I read in one of those "life after humans" books that glass and ceramics could survive millions of years because they're chemically similar to fossils. But geological processes could grind them to dust, I suppose. Sadly, the clearest archaeological evidence of our existence will be the mass extinction we've caused.
Interesting how games have portrayed this.... Playing Horizon Zero Dawn and that's supposed to be set 1000 years or so after the fall of our time and there's little to no evidence of buildings anywhere on the map, there's a few skyscrapers but all that is left of them is damaged facade and plants have crept up the sides and taken over everything. I wouldn't use the game as a guide but it's interesting. There was a TV show "Life after humans" and that was interesting.
From what I read in the book, I doubt any skyscrapers would last even that long without care and maintenance. There's certainly no way that, say, the Statue of Liberty could survive 2000 years for Charlton Heston to stumble across it. Well, unless it had been buried the mud and only recently exposed by erosion, or something.
Well POTA took a few liberties for artistic license. In that setting it works. Nature will take over once humans are gone, and almost none of our buildings will survive without care and maintenance. I do wonder what will take over this world when we're all gone.
If they survive, I think elephants have a pretty good shot. Some scientists think they're potentially as intelligent as we are, lacking only a symbol system to let them preserve and transmit knowledge -- writing, essentially. It's a fascinating idea, that intelligence isn't just about the sophistication of an individual mind, but the ability of different minds to share and preserve knowledge so they can work together to achieve more than any solitary individual, and can build cumulatively on each other's knowledge and innovations rather than everyone having to start over from scratch. Of course, if we die off in a mass extinction, we'll probably take the larger land mammals with us. The survivors would probably be the same guys who survived the last mass die-off: the birds. They're small and reproduce quickly, which is an edge for surviving a drastic environmental change that reduces food supply and demands rapid evolution/adaptation. And they're already pretty smart, and have already diversified once to fill a large variety of niches. So if we kill off ourselves and the major mammals, that will leave those niches open for the birds to fill once again. Which basically means the dinosaurs will be back in charge, baby.
Pandas, at least the giant variety, would be unlikely to survive a mass extinction. Their diet is so restricted and calorically limited, and their reproduction is so slow and inefficient, that they'd have died out long ago if they hadn't found themselves a cushy environment with abundant food and few threats. They're basically hothouse flowers, which is why they've been so critically endangered by the loss of much of their environment. But then, land megafauna like elephants would be unlikely to survive a mass extinction either. As I said, it's the small, light-eating, quick-breeding species that bounce back best from drastic environmental change, which is why the birds and puny mammals came through the K-T extinction while the larger, non-avian dinosaurs died out. Meanwhile, in the oceans, we've got octopus and squid, which seem to have highly sophisticated brains that may equal or surpass ours in some ways, but also have very short lifespans so that they don't have time to learn much or expand their capabilities much. Imagine a race of geniuses that all died before they could reach kindergarten -- all that wasted potential. It's kind of sad. But if they ever mutate in a way that lets them live longer, watch out. They not only have sharp, adaptable brains, but manipulative capability that makes our much-vaunted hands seem clumsy in comparison. On the other hand, they're very different from intelligent vertebrates in that they aren't social by nature, so they might not be inclined to form any kind of civilization. But on the, err, third tentacle, they might be smart and pragmatic enough to see the mutual benefit of cooperation. Whether they'd have any empathy for the other species they shared the planet with, like us, would remain to be seen.
Look at whale cortex gyrification and imagine what they might be able to do if they had arms and fingers...
Or probosces as dextrous as an elephant's, or tentacles as versatile as a cephalopod's. Let's not be primate-centric.
That's probably Rick Sternbach's famous painting from the cover of Future Life. http://sayhellospaceman.blogspot.com/2014/08/dolphins-in-space-gallery.html