The rate of an $S_N1$ reaction depends on the stability of the carbocation intermediate formed during the first (rate-determining) step. Heterolytic cleavage of the C-Br bond in each option yields the following carbocations:

1. $\text{C}_6\text{H}_5\text{-C}^+\text{H-C}_6\text{H}_5$: Secondary carbocation, stabilized by resonance from two phenyl rings.
2. $\text{C}_6\text{H}_5\text{-C}^+\text{H-CH}_3$: Secondary carbocation, stabilized by resonance from one phenyl ring and hyperconjugation from one methyl group.
3. $\text{C}_6\text{H}_5\text{-C}^+\text{(CH}_3\text{)-C}_6\text{H}_5$: Tertiary carbocation, highly stabilized by resonance from two phenyl rings and hyperconjugation from one methyl group.
4. $\text{C}_6\text{H}_5\text{-C}^+\text{H}_2$: Primary carbocation, stabilized by resonance from one phenyl ring. The carbocation formed from $\text{C}_6\text{H}_5\text{C(CH}_3\text{)(C}_6\text{H}_5\text{)Br}$ is the most stable because it is a tertiary carbocation further stabilized by extensive resonance delocalization over two phenyl rings. Therefore, it is the most reactive towards $S_N1$ substitution.