The city of San Cristóbal de La Laguna in the Canary Island of Tenerife (Spain) is of exceptional value as the first unfortified colonial city to follow regular plan - a grid, outlined by straight streets that form squares - in the overseas European expansion. It constitutes a historical example of the so-called "Town of Peace", the archetype of a city-republic in a new land that employed its own natural boundaries to delimit and defend itself. Founded in 1496, the historical centre of the old city was declared a World Heritage Site by UNESCO in 1999. We analyse the exact spatial orientation of 21 historic Christian churches currently existing in the old part of La Laguna, which we take as a good indicator of the original layout of the urban lattice. We find a clear orientation pattern that, if correlated with the rising or setting Sun, singles out an absolute-value astronomical declination slightly below 20°, which, within the margin of error of our study, might be associated with the 25th July feast day of San Cristóbal de Licia, the saint to whom the town was originally dedicated. We also discuss at some length some recent proposals which invoke somewhat far-fetched hypotheses for the planimetry of the old city and conclude with some comments on one of its outstanding features, namely its Latin-cross structure, which is apparent in the combined layout of some of its most emblematic churches.