A study of nuclei with few nucleons outside the closed shell provides benchmarks for the nuclear shell model especially in this modern era of physics where exotic doubly magic nuclei can be tested. The subject of this thesis is to experimentally investigate the properties of nuclei near 78Ni and to confront them with the predictions of modern large scale shell model calculations. In this regard, an experiment was performed at the National Superconducting Cyclotron Laboratory (NSCL) to measure excited states in 71-73Ni populated via the beta-decay of 71-73Co. Data collected from this experiment lead to partial level schemes for 71Ni and 73Ni and to improvements of existing level schemes for 70Ni and 72Ni. An objective of this experiment was to investigate the changes in excitation energy of the 5/2- state relative to the 9/2+ ground state as well as the search for the 1/2- isomeric state in odd-mass nickel isotopes approaching 78Ni. A second experiment was performed also at the NSCL where a two nucleon removal reaction from 73Cu was used to populate the low lying yrast states in 71Ni. Results from this in-beam experiment aided in constructing the level scheme of 71Ni. Systematics in shell model calculations using realistic interactions for odd mass 69-77Ni reveal a steady increase in energy spacing between the 1/2- level and 9/2+ ground state - suggesting an increased role of the g9/2 correlations, but an almost constant energy separation between the 5/2- and 1/2- excited states. Using data from the two experiments, the position of the 5/2- state in 71Ni and 73Ni and 1/2- state in 71Ni were identified. The decay of 74,76Ni into 74,76Cu was also investigated. Low lying states revealed new level schemes which are presented with an interpretation of the position of 1+ states populated via allowed GT transitions. A second project in this thesis is on the design and development of a detector system using a dual micro channel plate configuration. The system was built to detect and measure nanosecond isomers in neutron rich 73-76Cu and 76Zn isotopes. The design of the instrument and preliminary beam and alpha source tests done on the system are discussed.