A generalized compressibilty chart will quickly give you a good "feel" for where you can apply the ideal gas law. Have a look at the figure on page 6 of the document
For air at 20 deg C your reduced temperature is about 2.2. From this chart I would estimate that the ideal gas law will give you answers to within 2 or 3% all the way up to 2,000 psi.
While the chart is the best way to quickly get an overall feel for the situation, you can also use a simple Equation of State like Peng Robinson to estimate the compressibility. If PR gives an answer close to 1.0 then you know ideal behavior is a reasonable assumption. You can download the free units converter program "Uconeer" from my web site (see signature below) and use the Peng Robinson calculator built into it to estimate densities of common gases.
Of course it depends on why you need the density. If you are sizing air lines then you do not need extreme accuracy. The data you use must suit the application.