Template-synthesized silica nanotubes offer a unique and interesting opportunity for studying fluids in confined spaces. Their versatility stems from our ability to independently vary the inside diameter and surface chemistry. In this work we investigated capillarity for binary mixtures of water and methanol in hydrophobic nanotubes with internal diameters of both 30 and 170 nm. An improved sol-gel template synthesis process was used to prepare silica nanotubes with smooth and uniform walls within the pores of alumina template membranes. The pore diameter and thickness of the template membrane determined the outer diameter and length of the nanotube, respectively. The number of deposition cycles controlled the wall thickness. An octadecylsilane coating was selectively applied to the nanotube interior while leaving the nanotube exterior unmodified. The interiors of hydrophobic nanotubes prepared in this way were then labeled with trace amounts of adsorbed dyes. The diffusion of the dye molecules inside individual immersed nanotubes was investigated using fluorescence recovery after photobleaching (FRAP) experiments. Dye diffusion was used to determine the wettability of the nanotube interior as a function of solvent composition. Several important observations are reported here. First, a clear transition is observed in which all nanotubes change from non-wetting to wetting when the methanol mole fraction approaches 0.5. This transition appears at the same solvent composition for both nanotube sizes. Interestingly, the Young-Laplace equation fails to accurately predict the wetting transition. The difference between the observed and predicted wetting transition may be due to reliance on macroscopic values of contact angles or surface tensions in our predictions or may be related to the presence of liquid phase instability, dry-layers or non-spherical menisci within the hydrophobic pore.