  Pulsar Timing Arrays (PTAs) use high accuracy timing of a collection of low
timing noise pulsars to search for gravitational waves in the microhertz to
nanohertz frequency band. The sensitivity of such a PTA depends on (a) the
direction of the gravitational wave source, (b) the timing accuracy of the
pulsars in the array and (c) how the available observing time is allocated
among those pulsars. Here, we present a simple way to calculate the sensitivity
of the PTA as a function of direction of a single GW source, based only on the
location and root-mean-square residual of the pulsars in the array. We use this
calculation to suggest future strategies for the current North American
Nanohertz Observatory for Gravitational Waves (NANOGrav) PTA in its goal of
detecting single GW sources. We also investigate the affects of an additional
pulsar on the array sensitivity, with the goal of suggesting where PTA pulsar
searches might be best directed. We demonstrate that, in the case of single GW
sources, if we are interested in maximizing the volume of space to which PTAs
are sensitive, there exists a slight advantage to finding a new pulsar near
where the array is already most sensitive. Further, the study suggests that
more observing time should be dedicated to the already low noise pulsars in
order to have the greatest positive effect on the PTA sensitivity. We have made
a web-based sensitivity mapping tool available at http://gwastro.psu.edu/ptasm.
