Another fun one to do at restaurants is point at a random item on the menu and say "I'll have that!" Granted, there are places in the world I would not do this and I can only get away with it because I don't have any food allergies.
Hmm, that is too adventurous for me. If I can't at least guess what's in it, I'm not going to order it.
(No, I do not eat burgers and sausages or weird looking purees, creams or sauces, why?)
But I can imagine surprising yourself that way being quite fun!
I used to do the 'wander out at random and see where I wind up' thing in foreign countries. Results were varied, ranging from beautiful and interesting things I would otherwise never have found to serious physical danger. But I never got lost but a few times - my sense of direction is excellent and it's automatic to be aware of my backtrail.
The times I did get lost, all but one involved huge shopping centres or underground car parks, and it was really scary. The common factor seemed to be that I couldn't see the sky. My husband calls it 'getting malled'.
The one other time I got lost, I could see the sky well enough but it didn't help. I was in the very remote outback, and hit one of those areas where - direction becomes meaningless - is the best I can explain it. Never figured out why. So I just followed a gully until it led into a bigger gully, then followed that, and eventually came to somewhere that made sense and where directions worked normally. To this day I've never understood the mechanism, it was weird, and I suspect panicking would have been a really bad idea.
My sense of direction is horrendous. Despite this, I have always somehow managed to find the place I wanted to go to, eventually.
Well, there was one time (it was in the forest), when it was absolutely hopeless. I inadvertently managed to miss the spot by 15 kilometers and although I had ended up in a place I knew, I was too exhausted to walk back the whole way... My parents kindly fetched me.
But If I have the chance, I'd really rather not navigate. I feel I'm always so overcome by the details that I can't keep track of the whole picture. I could tell what a certain crack in a wall looks like, the pattern on the surface of a house, a leaf on the street, but reconstructing where I came from is a hopeless endeavor.
In cities there are also a lot of people and while I have gotten used to it a bit (I don't internally freak out anymore if someone approaches me from the front - i.e. our shoulders are parallel - or comes within a certain radius of my body) but it really distracts my brain.
I also have huge difficulties finding things I am looking for in general. It's like my brain just cuts them out of my field of vision...

I'm glad you made it out of that nonsensical place of no directions,
Róisín!
If you don't mind, could you try to explain what it felt like? And what it felt like in comparison to how you normally perceive directions?
It sounds very interesting!