Old tire…
Keep in mind it’ll be an indoor track at a university, so me bringing in a big tire all the time would probably not be allowed. 
Go to performbetter.com and find “The Trainer” under speed training. If not, you can use push up starts to develop specific starting strength.
If no hills, no sleds, I’d probably go for plyos like box jumps–and in fact I do, combined with hills.
What about a weight vest?
Weighted vest won’t work for accel purposes, too much vertical loading.
Hills also have vertical loading. If I was in that position, though, I’d probably go the plyo route, but not drop jumps and squat jumps for the reasons Charlie outlined in the Edmonton download.
Running up a flight of stairs is also an option, but there are risks associated with mis-stepping and falling. Depends on the rise and run of the stairs. You would want something with broader steps so that you did not have to be as accurate with your steps. Weigh your options and choose the best fit for you.
Incline treadmill?.
Depends on what you are using the hills for. If it is acceleration, do not use a treadmill. If it is for general conditioning and work capacity, possibly. I’m not a big fan of treadmills, aside from an alternative indoor form of doing tempo runs.
You could use it while doing vertical jumps, not something I would use, but I have hills next to the track so don’t need to.
I would watch out for negative effects on the direction of force application when using a vest. It’s also a different stimulus for acceleration when using a vest.
I would focus more on the short sprints from various positions, box jumps up, shot throws+hops. If you can find someone to help you out you could always do harness runs.
Multi level parking garages can sometimes be a good source of hills in winter. Pros: They are dry and often lit at night, and somewhat warm if underground. Cons: Security may kick you out and the surface is concrete.
What about a treadmill?
Do a search on the forum for isorobic trainer.
Are you kidding?
Be resourceful, it will help you later in life as well.
Get a weight plate (25lbs.), tie a rope to it and then tie the other end to a belt.
look, I don’t see what the big deal here is. You do not need to do hills, or any resisted running. If you can’t do it then don’t.
Focus on various starting positions, very gradually increase the speed and intensity of the runs, and take the time to focus on other elements like weights, jumps, and medball throws to serve as your main stimuli for your gpp.
Do the stairs have to be continuous? E.g, could I run up a flight of 10m 3x (running back down fast) for the 30m runs? or?
Yep, I found mine on the side of a road then went to home depot and got a rope and chain for a few bucks.
use an eye bolt and 2 big washers.
Henk Kraaijenhof used parking garages for hill substitute. They also did a lot of sprint work inside shopping malls, since there were no indoor tracks at the time. This was done with Nelli Cooman.