Anything cell-based will be schtonk - cellphone systems rely on having more or less a clear line of sight (through air or light obstacles) to the next base station, that is why these are put on towers - and the base stations rely on a backhaul to function. This is either a cable link that will eventually rely on something above ground to function, or a directional, narrow beam radio link that relies on a partner antenna in a very defined place.
Satellite phones (not satellite internet links, too much aboveground infrastructure involved) are likely to work for a while - as long as the satellite does not need any attention from a ground control station to continue functioning.
As mentioned, there is always shortwave and longwave radio - however the bandwidth of communications possible this way is, just as it is with satellite phones, orders of magnitude too small to support casual, universal communications as you would get from the landline network, or the internet, or the cellular phone system.
The reason Cellphone systems, TV networks are done on VHF and higher frequencies (simply speaking, three and four digit megahertz) is exactly that such links can be made relatively directional and of limited reach, and that there is a lot of bandwith available. Literal bandwidth (range of frequencies you can use for your channel, eg 2401-2433MHz for 802.11b WiFi channel 1) and data bandwidth (how many bits of data you can get through per second) are interrelated. 209
This is not limited to 1bit/s per Hz even if it looks that way superficially - but going above that limit means a lot of technical complexity (eg 90s 56Kbit/s modem links or DSL over phone lines having much lower bandwith - the modems are actually complex as all heck internally). The point is, establishing a 20MHz wide channel on shortwave would make the whole shortwave band unusable for anything else in the surrounding area, and would interfere with other uses in a far wider perimeter.
Direct satellite links have other gotchas: They need sophisticated equipment. They are expensive to build, so the actual comms bandwidth available to a whole ecosystem is rather small. And they are slow, not from a bandwidth but from a latency perspective - radio waves are still limited by the speed of light, and satellites are far away in the context of modern, rather interactive communications protocols.
Buried landline-type infrastructure could be made serviceable by whoever really needs it, as long as shallow underground structures (think manholes in the sidewalks) are unaffected, and the end points of the cables and any locations where active, underground equipment (repeaters etc.) belonging to them needs to be fed power are accessible. 87