"What imputation method is the best choice" is alway dependend on the dataset you look at
Taking the mean, in general is a valid imputation method. As somebody already mentioned, it is easy to explain for publications and it has its advantages in computing speed.
Mean as a imputation method is a good choice for series which randomly fluctuate around a certain value/level.
For the series shown, mean doesn look appropriate.
Since it is also just one variable you cannot use classical multivariate algorithms as provided by mice, Amelia, VIM.
You would have to look especially at time series algorithms.
One simple, yet for your example good like approach would be a linear interpolation.
x <- c(1,8,12,14,NA,NA,19)
Here is the output for a linear interpolation:
 1.00000 8.00000 12.00000 14.00000 15.66667 17.33333 19.00000
This is probably a better result than the mean.
There are also more advanced time series methods in the imputeTS package (by me) or one in the forecast package (by Rob Hyndman)