We present measurements of the branching fractions and charge asymmetries (where appropriate) of two-body B decays to η(′) K*, η(′) ρ, η(′) π0, ωπ0, and φπ0. The data were recorded with the BABAR detector at PEP-II and correspond to 89×106 BB pairs produced in e +e- annihilation through the Υ (4S) resonance. We find significant signals for two decay modes and measure the branching fractions B(B+→ηK*+)=(25.6 ±4.0±2.4) ×10-6 and B(B0→ηK*0) = (18.6±23±1.2)×10-6, where the first error is statistical and the second systematic. We also find evidence with significance 3,5σ for a third decay mode and measure B(B+ →ηρ+)=(9.2±3.4±1.0)×10 -6. For other channels, we set 90% C.L. upper limits of B(B 0→ηρ0)<1.5 ×10-6, B(B+→η′K*+)<14×10 -6, B(B0→η′K*0)<7. 6×10-6, B(B0→η′K*0) <22×10-6, B(B0 →η′ρ 0)<4.3×10-6, B(B0→ηπ 0)<2.5×10-6, B(B0→η′ π0)<3.7×10-6, B(B0→ωπ 0)<1.2×10-6, and B(B0→φπ 0)<1.0×10-6. For self-flavor-tagging modes with significant signals, the time-integrated charge asymmetries are A ch(ηK*+)=+0.13±0.14±0.02 and Ach(ηK*0)=+0.02±0.11±0.02.