This paper presents the effect of transmit diversity on the initial and neighboring cell search time performance and the most appropriate transmit diversity scheme based on system-level simulations employing synchronization signals for the Long Term Evolution (LTE) downlink. The synchronization signals including the primary synchronization signal (PSS) and secondary synchronization signal (SSS) are the first physical channel that a set of user equipment (UE) acquires at the initial radio-link connection. The transmit diversity candidates assumed in the paper are Precoding Vector Switching (PVS), Cyclic Delay Diversity (CDD), Time Switched Transmit Diversity (TSTD), and Frequency Switched Transmit Diversity (FSTD), which are all suitable for simple blind detection at a UE. System-level simulation results show that transmit diversity is effective in improving the detection probabilities of the received PSS timing and PSS sequence in the first step and those of the SSS sequence and radio frame timing in the second step of the cell search process. We also show that PVS achieves fast cell search time performance of less than approximately 20ms at the location probability of 90% regardless of the inter-cell site distance up to 10km. Hence, we conclude that PVS is the best transmit diversity scheme for the synchronization signals from the viewpoint of decreasing the initial and neighboring cell search times.