Back to Baghdad was arguably the most realistic F-16 sim -- it even had an option to use a seperate monochrome monitor for radar -- but was extremely limited in scope and probably tough to find nowadays.
Falcon 4.0 and its offspring are fine choices but for the difficult learning curve -- no instant gratification here.
IL-2 and its recent sibling Pacific Fighters are outstanding but also on the technically intimidating side.
For the quickest (and probably cheapest) air combat fix go NovaLogic (F-22, F-16, MiG-29), JetFighter III or IV (although running without a 3Dfx card might prove troublesome) or almost any of the Jane's titles, particularly F-15 and F/A-18 Simulator.
Most are pretty old as asceding to the realism crowd's demand for more, uhhh... realism just about killed off the genre.