Assume you are in your local at this time today.
I'll play, but this sentence confused me. Am I in my "local" as in local pub? Because in that case I would just stay there until it stopped raining.
I actually did this once in college, I was grabbing a drink after class and it started snowing really hard and I didn't feel like walking back to my place, so I just decided to stay there until the snow stopped. It had been rather nice that morning and I just threw on a sweater, no hat, no gloves, no waterproof anything (bad move), at least I had my boots on. I got to the bar after class at about 2pm intending to have a beer and head home, then it started storming. Fast forward twelve hours, it's still coming down and they're closing up. I've got a monster tab and an even bigger buzz. I made alot of new friends and was nearly cut off several times throughout the night. I stumbled home in the blizzard, got home completely soaked and chilled to the bone, but I guess I learned some lessons, namely wear something waterproof and check the weather before heading out.
If I'm in my "locale" then that's a somewhat different story. I work and go to school in the post-apocalyptic hell hole known as Detroit, and live just outside city limits. Should I need to take shelter, I would look for an abandoned house (no problem finding one of those). Probably be able to scavenge some bedding, if not some evergreen boughs would help out. Should be more than enough stuff to burn for heat as well. Find a safe place to start a fire (old oven, a grill, piece of sheet metal) and wait things out.
If I'm where I usually hang out in the woods, it is highly unlikely that I wouldn't have some sort of bigger kit with me, but if it's only what I have on me, then I've got a paracord bracelet with about 20 feet of ungutted cord, at least two knives, and a firesteel. It would be more likely than not that I have my small kit in a camera case on my belt, but I sometimes throw it into a larger pack if I'm carrying one. If I have my kit then I have a space blanket and a contractor's trash bag, which would both make my life alot easier. I would quickly gather some wood and try to find a place to keep it as dry as possible, and depending on the severity of the weather I might use my outer layer to form a shelter if I didn't have the trash bag, but I would likely keep my jacket on. I would probably just make a debris hut using the cord and natural materials. Framework of branches, some evergreen boughs over it and then cover with whatever else I could find. Put a layer of duff (mostly pine needles where I hang out) on the ground and cover with more boughs.
This was good to think about, I think I'm going to make sure that I have a trash bag and my space blanket immediately on my person more often now.