Given their location on the Hertzsprung-Russell (H-R) diagram, thoroughly characterized subgiant stars can place stringent constraints on a wide range of astrophysical problems. Accordingly, they are prime asteroseismic targets for the Transiting Exoplanet Survey Satellite (TESS) mission. In this work, we infer stellar properties for a sample of 347 subgiants located in the TESS Continuous Viewing Zones, which we select based on their likelihood of showing asteroseismic oscillations. We investigate how well they can be characterized using classical constraints (photometry, astrometry) and validate our results using spectroscopic values. We derive luminosities, effective temperatures, and radii with mean 1σ random (systematic) uncertainties of 4.5% (2%), 33 K (60 K), and 2.2% (2%), as well as more model-dependent quantities such as surface gravities, masses, and ages. We use our sample to demonstrate that subgiants are ideal targets for mass and age determination based on H-R diagram location alone, discuss the advantages of stellar parameters derived from a detailed characterization over widely available catalogs, show that the generally used 3D extinction maps tend to overestimate the extinction for nearby stars (distance ≲500 pc), and find a correlation that supports the rotation-activity connection in post-main-sequence stars. The complementary roles played by classical and asteroseismic data sets will open a window to unprecedented astrophysical studies using subgiant stars.