MODFLOW is an open source code as i remember, but there are different GUI that are proper and only limited or trial versions are availble (gw vistas for example). As aforementioned USGS provide a free of charge GUI but it is not open source too.
The variable-density flow model SUTRA of the USGS is free. There is one commercial graphical user interfaces (GUI) for SUTRA, but you can do without it. There are several publications by Voss (its main developer) & Sousa, and also by many others,
The first release of SUTRA was described in Voss, C.I., 1984. SUTRA-Saturated unsaturated transport- A finite-element simulation model for saturated-unsaturated, fluid-density-dependent ground-water flow with energy transport or chemically-reactive single-species solute transport, US Geol. Survey Water-Res. Inv. Rept. 84-4369, 409 p. There is a new release available now from the USGS.
For sharp-interface modelling, you can get, also free from the USGS, MODFLOW with the SWI2 package (Bakker, M., F. Schaars, J.D. Hughes, C.D. Langevin and A.M. Dausman (2013) Documentation of the seawater intrusion (SWI2) package for MODFLOW: U.S. Geological Survey Techniques and Methods, book 6, chap. A46, 47 p.).
You can try PMWIN (Processing MODFLOW for Windows). Latest version is not public domain. However, earlier version for example PMWIN5.0 is free. So, you can try this GUI for your work.
Alternatively, now you can get another free GUI from USGS. Thai is ModelMuse and it is easy to learn and use.
Nevertheless, FEFLOW is based on finite element scheme, but MODFLOW is based on finite difference scheme. So, it is your choice, which suits best for your work before choosing your package.
For open source GW modeling, you can go for USGS MODFLOW and its several packages and their GUI ModelMuse. No payment and great modeling with significant users group. You can get lots of help.
You can also find a free version of PMWIN (Processing MODFLOW for Windows) in the net.
However, if you want to do finite element package for GW modelling (like FEFLOW), there is no free package available. It is important to note that MODFLOW uses finite difference scheme.
One more information that if you want to model integrated surface water and groundwater modelling together, you can go for GSFLOW and MODELMUSE as GUI developed by USGS. Its totally free software and widely used by researchers around the world.
As previously said, ModelMuse is a completely free GUI developed by USGS and relies on MODFLOW computational code. It's quite different from Groundwater Vistas, for example, but I think it is easier to use and has more integration with GIS data than other software.
Regarding that Rodolfo said, an GIS integrated option and open source is FREEWAT. This GIS-based plugin, integrated in QGIS, has pre- and post- processing tools to analyse your data (including hidrochemical data analysis) and tools to run a MODFLOW model. All in the single GIS platform.
More info about FREEWAT, you can see the project link: http://www.freewat.eu
To download FREEWAT: http://www.freewat.eu/download-information