For a parallel plate capacitor with area A, separation d between the plates and a medium of permittivity εr between the plates, the capacitance C is given by,

C = ε0εr (A/d); where ε0 is the permittivity of free space.

So, high permittivity provides higher capacitance

If you want a material with very large dielectric constant try Calcium Copper Titanate. We used it for other purposes, but we did measure the dielectric constant and it was on the order of 10000. It is easy to make using a sol gel method and you can deposit it on glass, quartz, alumina, silicon or many other more exotic substrates.:

Article Controlling the preferential orientation in sol-gel prepared...

This will let you get very large capacitance in small devices.