Firstly, it is almost certainly better to use the original counts (Poisson regression assumes whole numbers). If you divided by time (i.e. counts per hour or day), you can use a log-time offset (in fact, you would want to do that for animal counts).
Secondly, if you really must analyze the mean rates (e.g. you did not retain the underlying counts), you would probably want to log-transform the mean rates. However, the annoying thing would be that higher values should have higher variance (the sampling distribution would for the observed log rate under a Poisson distribution is asymptotically normal with mean true log rate and standard deviation 1/sqrt(observed count)).
Thirdly, observations from the same spot are almost certainly correlated, you could either just sum them up to a total count, which would be fine if there are no differences between the two separate observations per spot that you want/can take into account. Or you model them as separate count data observations, but at a minimum you would want to take the correlation into account by e.g. adding a location random effect on the intercept of a Poisson regression model. You can go further by modeling the spatial correlation (presumably counts at spots that are less far apart are correlated, because the same animals are more likely to wander from one spot to the other, plants are more likely to spread there etc.).
Finally, how do you put distance into the model? E.g. a non-linear function like a spline function might be worth considering.