The C - C bond length is maximum in:

In diamond, all carbons are $s{p}^{3}$ hybridised and hence bond lengths are similar to carbon-carbon single bonds.
Graphite, ${C}_{70}$ and ${C}_{60}$ forms of carbon have delocalisation of electrons which leads to double bond characteristics. Hence, their bond lengths are in between carbon-carbon single and double bonds.
Hence, diamond with only single bond character will be have the longest bond.