There are several greener alternatives such as: diethoxymethane (DEM), various alkoxyethanols, Butyl diglyme (or diethylene glycol dibutyl ether), 2-methyl THF, and benzotrifluoride. I do not think many of these alternatives are considerably cheaper.
To David: Ph-CF3 is NOT green solvent (look at enviroment profile)
After H2O and CO2 , PEG, PPG and propylenecarbonate are most fit to green solvent definition. 1-methoxy-2-propanol, 3-methoxy-3-methyl-1-butanol and 2-methoxy-naphthalene are good as well.
2-Methyl THF is obvious environment-friendly in nature and could be better alternative to THF but it is costlier when compared to THF. It is good solvent for organic-water phase separations and low temperature reactions. So someone first check the reaction conditions before using 2-methyl THF.