Modern tissue engineering requires not only degradable materials promoting cell growth and differentiation, but also vascularization of the engineered tissue. Porous polylactide/polycaprolactone (PLA/PCL, ratio 3/5) foam scaffolds were prepared by a combined porogen leaching and freeze-drying technique using NaCl (crystal size 250–500 µm) and a water-soluble cellulose derivative (KlucelTM E; 10–100% w/w relative to the total PLA/PCL concentration) as porogens. Scanning electron microscopy, micro-CT, and Brunauer–Emmett–Teller analysis showed that all scaffolds contained a trimodal range of pore sizes, i.e., macropores (average diameter 298–539 μm), micropores (100 nm to 10 μm), and nanopores (mostly around 3.0 nm). All scaffolds had an open porosity of about 90%, and the pores were interconnected. The size of the macropores and the nanoporosity were higher in the scaffolds prepared with Klucel. Nanoporosity increased water uptake by the scaffolds, while macroporosity promoted cell ingrowth, which was most evident in scaffolds prepared with 25% Klucel. Human adipose-derived stem cells co-cultured with endothelial cells formed pre-vascular structures in the scaffolds, which was further enhanced in a dynamic cell culture system. The scaffolds are promising for the engineering of pre-vascularized soft tissues (relatively pliable 10% Klucel scaffolds) and hard tissues (mechanically stronger 25% and 50% Klucel scaffolds).