The interplay between charge order and superconductivity has been a long standing puzzle in a wide range of superconducting materials. The transition metal dichalcogenide 1T-TiSe2 is an interesting material that can give an important contribution to this debate. Indeed, 1T-TiSe2 undergoes a charge density wave transition and does also become superconducting upon Cu intercalation with a maximum transition temperature of 4.1 K. In this work we present a low temperature scanning tunneling microscopy/spectroscopy study on CuxTiSe2 (0≤x≤0.07). Our main results include the identification of single atom defects as well as Ti and Cu intercalation sites. This provides unique atomic scale information on the local crystal structure (1T vs 2H polytype) and precise registry of the CDW with the atomic lattice. We observe a striking instability of the CDW towards stripe formation. We measure the superconducting gap near optimal Cu intercalation and find no obvious correlation with the local CDW phase.