We consider the problem of sensor placement for estimating the direction of arrival of a narrow-band source randomly located in the far-field of a planar antenna array. Performance is evaluated by means of the expectation of the conditional Cramer Rao bound, normalized to that of the uniform circular array. Two cost functions are obtained, relative to azimuth and elevation, respectively. They depend on the array geometry as well as the distribution of the source azimuth. A class of uniform antenna arrays is investigated. It is adapted to the particular probabilistic distribution of the azimuth, while ensuring protection against array ambiguities. Using an exhaustive search procedure, we either seek the same reduction of both cost functions, or rather focus on one in particular. In the first approach, we achieve a reduction of almost 36% of both, regardless of the source azimuth distribution. In the second approach, we can obtain larger reductions for the targeted parameter. In both cases, optimal arrays are close to the V shape, for which performance analysis is conducted and closed-form expressions are obtained.