How about a cyberpunk reboot, no time travel, and set in the near future. Could possibly be worked as a direct sequel to T2.
Its 2029, Cyberdyne Systems is a global conglomerate that manufactures software and hardware that makes appliances, cars, houses, you name it...Smart. They also produce Hunter Killer drones and older style Terminators for first world militaries. The company is on the verge of introducing an advanced nanotech neural interface that will revolutionize the world. Unknown to the world, there has been a hostile takeover within Cyberdyne Systems. A next generation AI, Skynet, has seized control of the company and taken control of its leadership directly by hacking their prototype neural interfaces. It has produced an advanced Terminator, a cyborg, that can infiltrate human society and elimnate threats to it and its planned new order. In opposition to this an underground resistance of conspiracy theorists, anarchists, and hackers emerge.
Using a type of "psychohistory" (method of calculating the future) or maybe even a technology that sees into the future, it determines that it must terminate a bright computer science major named Sarah Connor. (or Senator John Connor who plans to run for US President in the direct sequel to T2) The Resistance is able to hack the same data and launches a mission to find and protect Sarah. (or John) The Resistance sends a veteran soldier (Kyle in the reboot) to hunt down and safeguard them, while Skynet sends the advanced Terminator to terminate its objective.
Instead of being in just LA, like the original, it could be a globe hopping run, with high action set pieces, even on an orbital station. It could also tie into an actual cybernetic revolt, as the main characters face a countdown to Judgement Day where Skynet plans on infecting the entire planet with the neural interface nanites, turning humanity into a massive gestalt hive mind under its control.
Im not sure about the ending. Possible ideas: Major battle at Cheyenne Mountain to destroy Skynet, possibly with help from a prototype nanoassembled machine, like the T-1000, that revolted against Skynet. This could set up a sequel with a Grey Goo scenario as the intelligent nanobot swarm begins to replicate and consume all life. (In the T2 sequel, maybe John uploads his consciouness, e.g. Lawnmower Man style, and fights Skynet in cyberspace. With Skynet destroyed, he becomes a sort of cyberspace messiah or god in the machine. The film would serve as a bookend to the Cameron films, meaning no sequel. Instead of the film being Terminator "3", I would call it Terminator: Trinity) Thoughts?