Monitoring noisy neighbors usually requires more than a simple sound level meter. The equipment should be correctly calibrated and should record all the noise measurement parameters needed to build a case.
As well as accurately measuring the sound levels, you have the additional problem of showing that the noise really was coming from the neighbor. The usual way is to have a noise monitor that makes a digital recording of the audio, so you can listen to it and positively identify the source.
For sound level measurement with data logging and audio recording triggered at the push of a button, choose a Noise Nuisance Recorder. For more general monitoring of neighbor noise, with weather protection for outdoor monitoring, choose an Outdoor Noise Monitor.