Context. Accurate stellar parameters are needed in numerous domains of astrophysics. The position of stars on the Hertzsprung-Russell diagram is an important indication of their structure and evolution, and it helps improve stellar models. Furthermore, the age and mass of stars hosting planets are required elements for studying exoplanetary systems. Aims. We aim at determining accurate parameters of a set of 18 bright exoplanet host and potential host stars from interferometric measurements, photometry, and stellar models. Methods. Using the VEGA/CHARA interferometer operating in the visible domain, we measured the angular diameters of 18 stars, ten of which host exoplanets. We combined them with their distances to estimate their radii. We used photometry to derive their bolometric flux and, then, their effective temperature and luminosity to place them on the H-R diagram. We then used the PARSEC models to derive their best fit ages and masses, with error bars derived from Monte Carlo calculations. Results. Our interferometric measurements lead to an average of 1.9% uncertainty on angular diameters and 3% on stellar radii. There is good agreement between measured and indirect estimations of angular diameters (either from SED fitting or from surface brightness relations) for main sequence (MS) stars, but not as good for more evolved stars. For each star, we provide a likelihood map in the mass-age plane; typically, two distinct sets of solutions appear (an old and a young age). The errors on the ages and masses that we provide account for the metallicity uncertainties, which are often neglected by other works. From measurements of its radius and density, we also provide the mass of 55 Cnc independently of models. From the stellar masses, we provide new estimates of semi-major axes and minimum masses of exoplanets with reliable uncertainties. We also derive the radius, density, and mass of 55 Cnc e, a super-Earth that transits its stellar host. Our exoplanetary parameters reflect the known population of exoplanets. Conclusions. This work illustrates how precise interferometric measurements of angular diameters and detailled modeling allow fundamental parameters of exoplanet host stars to be constrained at a level permiting analysis of the planet's parameters.