La2Ni7 is an itinerant magnetic system with a small ordered moment of similar to 0.1 & micro;B/Ni and a series of antiferromagnetic (AFM) transitions at T1 = 61.0 K, T2 = 56.5 K, and T3 = 42.2 K. M(H), and rho(H) isotherms as well as constant field M(T) and rho(T) measurements on single-crystalline samples manifest a complex, anisotropic H-T phase diagram with multiple phase lines. Here we present the growth and characterization of single crystals of the La2(CuxNi1-x)7 series for 0 x 0.181. We measured powder x-ray diffraction and composition, as well as anisotropic temperature-and field-dependent resistivity, temperature-and field-dependent magnetization, and temperature-dependent heat capacity on these single crystals. Using the measured data we infer a transition temperature-composition (T-x) phase diagram for this system to study the evolution of the AFM ordering upon Cu substitution. For 0 x 0.097, the system remains magnetically ordered at base temperature with x 0.012, showing signs of multiple AFM ordering temperatures. For the higher substitution levels 0.125 x 0.181, there are no signatures of magnetic ordering, but anomalous features in resistance and heat capacity data are observed which are consistent with the Kondo effect in this system. The intermediate x = 0.105 sample lies between the magnetic ordered and the Kondo regime and is in the vicinity of the AFM quantum critical point (QCP). Thus, La2(CuxNi1-x)7 is an example of a small moment system that can be tuned through a QCP. Given these data combined with the fact that the La2Ni7 structure has kagomelike, Ni sublattices running perpendicular to the crystallographic c axis, and a predicted 3d-electron flat band that contributes to the density of states near the Fermi energy, La2(CuxNi1-x)7 becomes a promising system to host and study exotic physics.