The cheapest way to see F1 cars in action is to go to a test day, the big snag with this is that they only really test in Europe but if your European vacation happens to coincide with testing at say Silverstone, Hokenheim, etc, etc. Its not very glam but you still get the noise and some of the spectacle.
I suspect the most reasonably priced races are going to be at places like Brasil, China, maybe Turkey and in Theory if you get a cheap hotel in France and then sneak into Monte Carlo early and find your self a vantage point (probably need to get there in the small hours) its possible but not easy to do Monaco for peanuts!
Of course when you factor in the air fare it might actually be cheaper to get a grandstand ticket at the race in Indy but were is the fun in that?
