Roosevelt Island (which is a part of the Manhattan borough) actually has an underground, pneumatic trash collection system: https://untappedcities.com/2020/04/09/inside-roosevelt-islan... . I think it would be hard to retrofit such a thing onto the already-built-up parts of the city though.
> I think it would be hard to retrofit such a thing onto the already-built-up parts of the city though.
It would be prohibitively expensive, because there's no master record of which pipes/wires/cables/etc. exist in any given location. It's very expensive to dig in Manhattan[0], because you basically have to dig carefully and see what's actually there, rather than having some knowledge of "the gas pipes are in this spot, so we can dig around them". So much of the infrastructure was installed before detailed record-keeping was standard practice.
As far as trash collection in NYC, the main thing that needs to happen is containerized trash collection. Right now, trash bags are just left on the sidewalks 3-5 times per week for 12 or more hours at a time, creating an absolute buffet for rodents.
[0] This actually applies to most of the city, but Manhattan is a combination of the oldest-built and most-densly-built infrastructure, so it's particularly expensive there.
Many cities face the same problem and this is how they fix it: they make a plan to rework every pipe and wire in their city in a finite amount of time. They go block by block and tear it all up at once. They bring a shitload of guys and equipment instead of two idiots with jackhammers, so the whole thing is ripped out and replaced in a week instead of in 5 years.