α-CsPbX3 (X = Cl, Br, I) 2D nanostructures are widely used in solar cells, photocatalysis and photovoltaic applications, mainly because of their high efficiency in the conversion of solar energy. Based on hybrid Density Functional Theory (DFT) calculations we consider two aspects, (a) the role of surface termination, and (b) that of quantum size (thickness) of the 2D slabs. We show that the surface termination is a key aspect in determining the electronic properties. For the (001) surface of α-CsPbX3 perovskites there are two possible terminations, with similar stabilities but different positions of the band edges. In general, the band edges of the (110) surfaces, with the X-terminated surface being the most stable one, are lower in energy than the (001) ones. These conclusions are very important for the design of efficient heterostructures for solar light harvesting. Furthermore, the properties of α-CsPbX3 2D nanostructures can be tuned by varying the thickness. We present a general model to predict quantum size effects of α-CsPbX3 from ultrathin films (3-5 atomic layers) to the bulk. Finally, based on calculated electronic properties of CsPbX3 (and TiO2 surfaces), we estimate a type-II alignment in composites such as CsPbX3/TiO2, favourable for electron migration from the perovskite to TiO2. These results can help the rational design of halide perovskite nanostructures for solar energy harvesting, in particular by interfacing 2D materials with specific surfaces and terminations.