The openSMILE audio feature extraction toolkit may be able to provide the functionality you desire, where the input is a .wav file and the output extracted audio features. See: http://audeering.com/technology/opensmile/
openSMILE provides a command line executable that is coupled with a configuration file that defines the features to be extracted. The executable has binaries for Linux and Windows (32 bit), and I've also built the executable from source for use on macOS. It provides its own objects that calculate features such as MFCCs, energy, pitch, but also "chroma" musical features (which may help with music classification). It comes with many prebuilt feature configurations that have been used for audio classification tasks, such as the Audio Visual Emotion Challenge (http://sspnet.eu/avec2017/).
Below is an example of how openSMILE can be used to extract features from a single .wav file and a chosen configuration. The
output.arff is a format used by the Weka machine learning library.
SMILExtract -C config/emobase.conf -I input.wav -O output.arff
Custom configurations can also be written using the openSMILE configuration language and also the extensive PDF documentation included with openSMILE's download.
This has the desired functionality as described in the original question:
looking for a way to take a .wav file and extract features from it that could be used for further classification