Next-generation wireless communication systems are unifying large-scale multiple-input multiple-output (MIMO) and integrated sensing and communication (ISAC) to enhance sensing and communication performance. In this paper, the signal detection problem for MIMO-ISAC systems is modeled as a mixed-integer least squares (MILS) problem. To solve it efficiently, we propose a projection-based neighborhood search-aided alternating direction method of multipliers (P-NS-ADMM) detection scheme. By theoretical analysis, we demonstrate that P-NS-ADMM achieves the same received diversity order as maximum likelihood (ML) detection. For further complexity reduction, an iteration-based NS-ADMM (I-NS-ADMM) is proposed to remove the complex projection operation. Complexity analysis shows its complexity advantage compared with P-NS-ADMM. Moreover, to better estimate the sensing signals for I-NS-ADMM, a flexible mechanism of ADMM iterations is given. Finally, simulations demonstrate the proposed NS-aided ADMM detection schemes have significant performance advantages in terms of both BER and NMSE.