Answer:
I imagine myself being proposed to during a walk in the woods. As I live near a forest area, I would love to go on a picnic through the woods, and whilst we are hiking, I would be completely unaware of the future events to take place. Me and my (maybe) future spouse would climb near a nice grassy open area preferably near a stream (because water is cool), and eventually I would be proposed to.
I doubt I would be proposed to, as I think I am more likely to propose to someone I feel connected to. I'm particularly picky about people, so it's very unlikely for me to accept any kind of proposal.
The way I imagine proposing to someone is to announce that I have to be out late for work one night, perhaps for overtime or some other circumstance. I would ensure that I got home at a particularly late time, and whilst the person is asleep, would set up a display in a part of the house that I decide. In the morning, I would have to make sure to get up before them, and I would make breakfast for them to make sure they stay in the room they were in. After eating, I would lead them into the displayed room with my hands over their eyes, and turn them around. I would get down on one knee and ask them the big question, and I would present them with a ring that they may have chosen sometime earlier. I don't like surprising people to an extent where they may feel stressed, so they would know I would be proposing sometime, they just wouldn't be sure exactly when. (And don't worry, I bought the ring)