The center position is the safest for a car seat. Not only is that somewhat logical (regardless of what side the car is impacted, there's distance between impact and child), but it is supported by research.
That same study also indicates there was no statistically significant difference in the injury risk between the two sides of the car, only between the center and side positions.
Seating position distribution for child occupants was as follows: left
outboard (31%), center (28%), and right outboard (41%)... Child
occupants seated in the center had an injury risk 43% less than
children seated in either of the rear outboard positions.
The injury risk was 0.27%, 0.17%, and 0.29% in the left outboard, center, and right outboard positions, respectively. No statistically significant difference in injury risk was found between child occupants in the right and left outboard positions; therefore, they were combined for additional analyses.
Kallan et al. Seating Patterns and Corresponding Risk of Injury Among 0- to 3-Year-Old Children in Child Safety Seats. Pediatrics, Vol. 121 No. 5, 2008.
That appears to hold true regardless of age -- the middle rear seat is safest.
The information from every fatal crash in the United States between
2000 and 2003 was analyzed.... The data show that the rear middle seat
is safer than any other occupant position when involved in a fatal
crash. Overall, the rear (2(nd) row) seating positions have a 29.1%
increased odds of survival over the first row seating positions ...
occupants of the rear middle seat have a 13% increased chance of
survival when involved in a crash with a fatality than occupants in
other rear seats.
Mayrose and Priya. The safest seat: effect of seating position
on occupant mortality. Journal of Safety Research, Volume 39,
Issue 4, 2008.
Of course, if the car seat can't install in the center, then you have to choose a side. Crash statistics don't have much to say about this, but this UK site indicates that the passenger side would be preferred, since you're then taking the child in and out on the sidewalk side (rather than standing in the roadway) when parallel parked. It also indicates that middle is safer in the event of a crash, but does not mention crash risks when choosing between two sides.
I will also note that whether or not it's true that drivers instinctively veer to protect themselves, that's only one type of potential crash. Head-on collisions are the most common, but you can be struck from anywhere -- and there isn't much that swerving can do to protect you from a side or rear impact. (Indeed, the numbers show that a driver-side impact is slightly more likely than a passenger-side impact...)
NHTSA crash statistics (for all collisions, not just injuries or fatalities) were averaged over multiple years to come up with the numbers. Data, and graphic, are from crashtest.com, found via the Internet Wayback Machine. Note that this is for the US, so driver is seated on the left side of the car.