You can go for different metal organic frameworks, that offer highly mobile transition metal ions in solution medium. They often attain high specific area, because of their microporous or nanoporous network.
An, Geon-Hyoung, Hyo-Jin Ahn, and Woong-Ki Hong. "Electrochemical properties for high surface area and improved electrical conductivity of platinum-embedded porous carbon nanofibers." Journal of Power Sources 274 (2015): 536-541.
Graphene oxide hydrogel used in a supercapacitor material with high electrical conductivity and high specific area. it showed a high electrical conductivity of 1351 S m−1 and a specific surface area of 745 m2 g−1. as detailed in the reference;
Article Synthesis of a highly conductive and large surface area grap...