How Far Can I See?

That really depends on how tall you are, what you're standing on, and how lumpy and cluttered the ground around you is. Let's assume, for the sake of argument, that you're levitating up over the vast and flat Billiard-Table Plains:

Eye Level (in metres)Horizon Distance (in kilometres)Notes
0.050.7Lying on your face in the dirt
0.1251.1
0.251.6Crawling on your belly
0.52.2Crawling on your hands and knees
13.2Sitting on the ground
1.53.9Average human eye-level, standing
24.5
35.5From horse-back
46.3
88.9Average storm-giant
1612.6
3217.9From a tall tower
6425.3
12535.3From the top of the very tallest trees in the Great Forest
25050
50070.7From an average hill-top
1000100
2000141.4From a small mountain-top
4000200
8000283From the top of the highest mountain peaks
16000400
32000566.6Not very much air up here

NOTE: To make life easier for myself, I've assumed a planetary diameter of exactly 5,000 kilometres. All horizon distances have been rounded to the nearest tenth of a kilometre (100 metres).

I've used data from this site to get the relevant figures.

Naturally, obstacles like walls, buildings, undulations in the ground, trees etc. are going to have a significant effect on what you can see, as will the height of whatever it is that you're looking at. For example, although an average human can only see about four kilometres before the horizon intrudes, they'd be able to see the top of a storm giant's head almost nine kilometres away... assuming, of course, that they could distinguish the teensy-tiny black speck as a storm-giant's head.