I suggest Madflow model USGS(PMWIN). In my opinion, this model is very suitable for simulating surface water and underground waters. If you have enough data and you can create a good conceptual model.
The University of Colorado provide an extensive list here of groundwater models (http://csdms.colorado.edu/wiki/Hydrological_Models). I would also add that the FreeWat project might suit your needs (http://www.freewat.eu/) as might some of the BGS models (http://www.bgs.ac.uk/research/groundwater/modelling/home.html)
I have Developed a new physics-based model for coupling surface water-groundwater, the DrainFlow, and I am happy to share it if you like to use it you study.
Article Development, testing and application of DrainFlow: A fully d...
Prickett, T. A., and. Lonngquist, C. G., (1971), “Selected Digital Computer Techniques for Groundwater Resource Evaluation”, (Illinois State Water Survey Bulletin 55.) 62 pp.
GSSHA model. Please refer to the following article for further details.
Wijayarathne, D.B., Gomezdelcampo, E., 2019. Using shallow groundwater modeling to frame the restoration of a wet prairie in the Oak Openings Region, Ohio, USA: GSSHA model implementation. Environ. Earth Sci. 78, 21