What reagents or series of reactions would allow for selective hydroxylation of an allylic methyl group outside of a ring?
As has been stated by @Beerhunter those benzylic hydrogens are a serious concern . Nonetheless, here is a different offering. To solubilize carboxylic acid 1 both the phenolic group and the acid should be protected. Here, both of the groups are protected as methyl groups. [An ester group and silylated (TBS?) phenol would also suffice.] The double bond of 2 is epoxided to 3. The critical step is the isomerization of the epoxide to an exo-methylene allylic alcohol. There are several reagents that do this transformation. Yamamoto1 has shown that methyl groups are more reactive than methylene groups with the epoxide rearranging reagent diethyl aluminum 2,2,6,6-tetramethyl piperidide although no benzylic methylene examples were provided. 
Acetylation of the allylic alcohol affords allylic acetate 4. Grieco2 has reported that bis-acetonitrile PdCl2 isomerizes allylic acetates to their tautomer in what is an equilibrium reaction favoring the more stable isomer. In this instance, the trisubstituted, endocyclic double bond compound 5 is expected. The remaining steps involve removal of the protecting groups of choice to afford the target 6.

1) S. Tanaka, A. Yasuda, H. Yamamoto and H. Nozaki, J. Am. Chem. Soc., 1975, 97, 3252. 

2) P. A. Grieco, T. Takigawa, S. L. Bongers and H. Tanaka, J. Am. Chem. Soc., 1980, 102, 7587.