We derive the star formation history in four regions of the Small Magellanic Cloud (SMC) using the deepest VI color-magnitude diagrams (CMDs) ever obtained for this galaxy. The images were obtained with the Advanced Camera for Surveys onboard the Hubble Space Telescope and are located at projected distances of 0.5-2 degrees from the SMC center, probing the main body and the wing of the galaxy. We derived the star-formation histories (SFH) of the four fields using two independent procedures to fit synthetic CMDs to the data. We compare the SFHs derived here with our earlier results for the SMC bar to create a deep pencil-beam survey of the global history of the central SMC. We find in all the six fields observed with HST a slow star formation pace from 13 to 5-7 Gyr ago, followed by a ~ 2-3 times higher activity. This is remarkable because dynamical models do not predict a strong influence of either the LMC or the Milky Way (MW) at that time. The level of the intermediate-age SFR enhancement systematically increases towards the center, resulting in a gradient in the mean age of the population, with the bar fields being systematically younger than the outer ones. Star formation over the most recent 500 Myr is strongly concentrated in the bar, the only exception being the area of the SMC wing. The strong current activity of the latter is likely driven by interaction with the LMC. At a given age, there is no significant difference in metallicity between the inner and outer fields, implying that metals are well mixed throughout the SMC. The age-metallicity relations we infer from our best fitting models are monotonically increasing with time, with no evidence of dips. This may argue against the major merger scenario proposed by Tsujimoto and Bekki 2009, although a minor merger cannot be ruled out.