I found an app that I think will work really well when I resume HIIT running this fall, when it's not 6 million degrees outside. I used a stopwatch last winter and it was a pain in the ass.
The app is called Seconds. Cost $5 for the full version. Free version won't remember your settings, so you have to set your timers every time you use the app. You set a timer for high intensity intervals, and a seperate timer for low intensity. There are also timers for a warmup and a cool down. The timers are all custom. You also specify a number of intervals. It also has functions for circuit training that I haven't tried out.
So if you wanted to jog for a few minutes to warm up, do 15 second sprints followed by 45 second walks or slow jogs, then a two minute cool down, you would just set the individual timers as such. When one timer ends, you get a signal (beeps or horns or vibrations and whatnot) and the next timer begins.
It's seems to work well so far. No weird hangups like I've had with other apps, like not working when my phone is asleep or locked. It also works when listening to music.