Context : The Tarantula Nebula ( a.k.a . 30 Dor ) is a spectacular star-forming region in the Large Magellanic Cloud ( LMC ) , seen through gas in the Galactic Disc and Halo . Diffuse Interstellar Bands ( DIBs ) offer a unique probe of the diffuse , cool–warm gas in these regions . Aims : The aim is to use DIBs as diagnostics of the local interstellar conditions , whilst at the same time deriving properties of the yet-unknown carriers of these enigmatic spectral features . Methods : Spectra of over 800 early-type stars from the Very Large Telescope Flames Tarantula Survey ( VFTS ) were analysed . Maps were created , separately , for the Galactic and LMC absorption in the DIBs at 4428 and 6614 Å and – in a smaller region near the central cluster R 136 – neutral sodium ( the Na i D doublet ) ; we also measured the DIBs at 5780 and 5797 Å . Results : The maps show strong 4428 and 6614 Å DIBs in the quiescent cloud complex to the south of 30 Dor but weak absorption in the harsher environments to the north ( bubbles ) and near the OB associations . The Na maps show at least five kinematic components in the LMC and a shell-like structure surrounding R 136 , and small-scale structure in the Milky Way . The strengths of the 4428 , 5780 , 5797 and 6614 Å DIBs are correlated , also with Na absorption and visual extinction . The strong 4428 Å DIB is present already at low Na column density but the 6614 , 5780 and 5797 Å DIBs start to be detectable at subsequently larger Na column densities . Conclusions : The carriers of the 4428 , 6614 , 5780 and 5797 Å DIBs are increasingly prone to removal from irradiated gas . The relative strength of the 5780 and 5797 Å DIBs clearly confirm the Tarantula Nebula as well as Galactic high-latitude gas to represent a harsh radiation environment . The resilience of the 4428 Å DIB suggests its carrier is large , compact and neutral . Structure is detected in the distribution of cool–warm gas on scales between one and > 100 pc in the LMC and as little as 0.01 pc in the Sun ’ s vicinity . Stellar winds from the central cluster R 136 have created an expanding shell ; some infalling gas is also detected , reminiscent of a galactic “ fountain ” .