It seems that pokemon tend to spawn in the exact same spot. From both my house and my workplace different pokemon keep appearing, but they always pop up in the exact same locations over and over again.
How long after I have captured a pokemon in a certain location will it be until another pokemon shows up?
There is no way to know.
Pokemon spawning is somewhat random. Even at the animated grass icons, which represent better chances of finding a Pokemon, there is still no guarantee you will run into one.
You can check "Nearby Pokemon" through the tab to the bottom right, to at least get an idea of the current Pokemon congestion. If 10 Pokemon show as "nearby", you have a better chance of running into more Pokemon than if it only shows 1. It is still no guarantee.
That said, if you go to an area with higher traffic1, you have better chance of running into Pokemon more frequently. In fact, when I go to the nearest train station, I almost always run into Pokemon in groups.
You can also increase your chances with the use of incense, or by using a Lure Module at a PokeStop.
1 "Traffic" referring to the means in which Niantic determine Pokemon spawn rates. Areas with higher traffic have higher spawn rates.
At my house I'm seeing two spawns every hour, always at 24 and 52 minutes after the hour (with a minute or two variance at most). No other natural spawns aside from those so very easy to track and capture as many of the 48 daily spawns as possible when I'm home and awake.
I'm not sure about refresh rate, but I have noticed that Pokemon tend to spawn at the same locations where you find XM in the Ingress game. I believe that as the Ingress map is used as a "base map" for Pokemon Go, you can with a fair amount of accuracy predict where Pokemon spawn by using the Ingress game and looking for XM spots near you.
Spawns at "spawn points" have differing frequencies by spawn point, but can be as frequent as every hour or as infrequent as daily. Spawn points will tend to have the same frequency, though, for the two week period until they're reset; for example, one near my house a few months ago had an every-two-hours spawn of Growlithes at one spot and an every-three-hours spawn at another nearby (meaning every six hours there were two next to each other). Spawns of non-commons that reappear more frequently than hourly are likely multiple spawns or cluster spawns (i.e., you're not seeing just one Pokémon spawn every 15 minutes, you're seeing four of them spawn on hour rotations).
Further, spawns that you do not catch will come back with some frequency across an hour period. This again differs by spawn; they have various patterns, but you can visualize it like so. If the hour is split into 15 minute periods denoted by letters ABCD, then some pokémon will appear as AC, for example, meaning they will appear for 15 minutes, disappear if you don't catch them, then 15 minutes later reappear. This will look like a 'new' pokémon, but it's actually the same one, and someone who already caught it will not be able to catch it.
The hourly mechanic is well explained in this PokemonGoHub guide to spawn points, although it oversimplifies some (as not all spawns are once per hour).
It seems the rarer the Pokemon, the longer the spawn time, I.e. Rare > Normal > Common but I am not sure exactly how much time each takes.
