I'm looking for another way to say, “I looked around, until my eyes landed on a man.” I’m sick of the sentence “I looked around”, but it’s important that she does since she wakes up in an unfamiliar place.
Instead of saying that your character is looking somewhere, you could use the opportunity to describe the situation and the scenery.
My eyes scanned the crowd for any familiar face. This proved difficult because almost everyone seemed to be wearing a hood.
My head pounded and I would have liked nothing better than to go back to sleep. But I didn't know how much time I had until my attacker came back. Time to do an inventory: The car appeared to be stranded in the middle of a forest, not a living soul inside. The gloves compartment contained a pack of cigarettes, but was otherwise empty. But I found a can of antifreeze under the seat. Could it serve as a weapon? Better than nothing, I suppose.
A sudden rustling noise caught my attention. Shit. He's back.
You describe the results of the character's actions.
Telling: I looked around.
Showing: I stood in the center of a crowded room, filled with the Glitterati, each more eager than the last to be seen doing good-works for the latest cause-celeb.
A way to ensure you are showing more than telling, is to start with an independent clause describing an action -- I stood in the center...' -- then describe the consequences of that action -- seeing all those people, in this case. The character could see them all by looking around. The thing you wanted to tell becomes the inevitable conclusion of your description.
And, you don't need to say 'I saw' or 'My eyes' because you are in a first person POV, so these things things are assumed.
There's no need to tell the reader that the character is looking at something. (I search for "look" in my stories during revision and usually rewrite those sentences.)
So, instead of "I looked around the room" or "I saw a red couch," I'd rewrite to "A red couch was in the corner, below a curtained window. A bookshelf held a single book. A man stood in front of it with a drink in his hand." The fact that the character is looking is implied and doesn't need to be said.
If they are looking around at something, put the object in place of “around” example:
I looked at the wide, long hallway. Nothing seemed out of the ordinary... but looks can be deceiving.
Now with I looked around.
I looked around at the wide, long hallway. Nothing seemed out of the ordinary... but looks can be deceiving.
It’s the same thing, without “looked around.” I hope this answers your question!