The answer isn't simple because you need more than physical distance and barriers to accomplish variation. It requires said distances and barriers to hold over long periods of time and allow for long periods of little contact as well. A good rule of thumb would be to take real distances as a starting template and then work through your constructed history to arrive at mixtures or backwards from a set of differences you want to achieve.
That said, we should be able to work backwards through our own history and at least get some numbers to work with.
That's a map taken from Wikipedia showing the distribution of Y-DNA haplogroups in European populations. Now, I don't really know what a haplogroup is, but as you can see, there is a clear racial and phenotypical distinction there. edit - Wesley Obenshein explains this more in the comments
Here's a link to a world map of the same: big picture
The issue here is, there doesn't seem to be a timelined map giving us how these distributions have changed over a few millenia (which is the smallest time scale necessary to make any conclusions - and that's still very generous).
What we do know is that even with relatively low tabooing of interbreeding, as has applied to our world for a few centuries and less as populations have grown, we still have pretty distinct racial appearances. You can still tell people apart and assume a genetic ancestry even when the differences are subtle. This means we can assume that barriers and distances don't need to be that large to maintain differences. How convenient :P
The question on minimum distance remains. Is there really a minimum distance however? Depending on whether you've got non-human races in there, many factors could contribute. According to this forum post for instance, sunshine is a determining factor in the levels of skin pigment. If the desert is in the middle and the world rotates around its star like ours does, it wouldn't matter if you're in the desert or not, but if you're around the equator or not, to get darker skin. That doesn't have to do with distance. Many such factors can be included, but this is overt enough to be easy to use.
So the minimum distance probably has to do more with population concentration and how much these populations operate as a whole or separately. A good way to work up to distances would be to distribute the land according to the success of each civilization. If they're more successful, give them more space and have all those inside that space be of the same race. Larger spaces will have higher tendency to include variations and individuals or communities from other races.
The last distribution implies that the minimum distance would depend on the total available space. But obviously, if there's too little space there might be little to no variation at all. If there's too little climate variation, there's less racial variation as well. So now the question becomes, how large can communities grow? Obviously this has a relation to technological level and resources/food.
Wikipedia gives us some numbers: http://en.wikipedia.org/wiki/Historical_urban_community_sizes
They range from a few thousand in Neolithic times to 50-100 thousand in the Iron Age. We could take population densities and the size of countries at those times as a reference, but those depend much more heavily on how much space and resources are available while the settlement sizes are a better indication of how many people are willing and capable of living together in stable populations. Lets take the areas covered by those settlements though, as it would be an indication of how close together people are willing to live.
Wikipedia states that one of the largest Neolithic settlements spanned 15 hectares, which is .15 square kilometers. That's a square about 400 meters on each side, which is not much. To compare, Babylon was about 9 square kilometers in size and had at one time up to 200 thousand people in it.
To get what you want, work backwards from these.
- Decide how large your area is and what the environment is like.
- Decide how rich each environment is.
- Then decide the technological level of the time.
- Match the technological level to a historical one and find out how large cities were.
- Make an estimate of the habitable area and then divide to see how many cities would exist in it.
- Halve that number to make room for empty space and concentration of populations (population densities per period will be helpful -> link to pdf of study).
- Multiply the average city population for the technological level with the cities to get the world population
- Rearrange population numbers based on technological success of each nation/race/area
- Reallocate the cities to match the new population numbers.
- Provide enough space for the cities to each race and arrange cities relatively evenly.
If by this time you get a lot of overlap or a very low population size, especially if it's low compared to technological level, you have too little space. But at least you can work backwards from how large your world is and how many different habitats are available (don't forget planetary tilt and rotation) using some real numbers to help.