I might be in the minority, but I'd adore a single-player Terminator game that put you in the shoes of the Terminator's target, rather than someone like a Kyle Reese analogue. Give me a small town, or a series of linked small environments, as the main play area, and randomise the Terminator's arrival in the first "act" (or base it on player actions going about their normal routine), then have a handful of potential sites that could allow the target to fight back and kill the Terminator and options for slowing it down.
For example:
Game opens with the player waking up in their apartment. Their job is at a small business a block or two away. The Terminator has already arrived, has your name and is working through the telephone directory. As it's at least partially randomised (though with a nudge to favour the player so you're not first on the list) the Terminator may already have killed the first poor sod who shares your name and be on its way to your apartment. Right. Now.
Your advantage right now is that you know that you're playing a game and that you should get moving to work, but you don't get the option to start gathering weapons or unlocking potential Terminator-killing locations until your first encounter with the machine - why would you, after all? You're just getting up to go to another day at work, not prepping for a life-or-death battle with a killer cyborg. The Terminator's appearance is randomised too, though to make things a little fair it will at least have a similar build each time, but you can't guarantee it's going to be a giant, white guy with a bulky coat and cropped hair so you'll have to be alert.
Maybe you leave your flat, get lucky and end up on the bottom of the list of names. Congratulations, you have time to make it to work where there are multiple exits, your boss keeps a pistol under the counter, and there are lots of NPCs to get in the way of that huge guy pounding across the store to get to you. Perhaps you're not so lucky, and you get ambushed on the walk to work and now you have to run, but at least that alley down there leads to somewhere you can hide for valuable minutes and shake the Terminator. Or maybe you're really unlucky and you mess about in your flat too long, your door crashes in on itself and you now have to scramble to get past this hulking, walking death machine, into the hall and down the stairs before it shoots you down.
Once you're on the run, the map opens up and locations like gun shops, tool stores and areas with large crowds or buildings with secure entrances open up. The police station is there, and if you get to it you have access to heavier weaponry, but you will be brought in to keep you "safe", which just traps you there with something hunting you...
The game could either run with a timer - the longer you stay alive, the more useful locations open up, until you get one where you can kill the Terminator, but then you still have to lure it there which is a risk in itself - or with players having to track down certain clues or items to unlock these areas. The key here is that these environments aren't massive sandboxes, but they're dense, crowded and built for replayability so that each player should have a reasonably novel experience each time, and the game should be built for player stories and sharing online.
Tense, time-critical chases where you are always outgunned, and you have to think fast to stay alive until the point where you can finally fight back, and even that final fight should be a risk.
