I'd second using US Census Data as was already mentioned in another answer.
As an additional source of government data with a bit more information about wages and income, you could also check out the aggregate ZIP code data provided by the IRS:
ZIP Code data show selected income and tax items classified by State, ZIP Code, and size of adjusted gross income. Data are based on individual income tax returns filed with the IRS and are available for Tax Years 1998, 2001, and 2004 through 2014. The data include items, such as:
- Number of returns, which approximates the number of households
- Number of personal exemptions, which approximates the population
- Adjusted gross income
- Wages and salaries
- Dividends before exclusion
- Interest received
I've used that to try to get at socioeconomic status in the past. It's helpful because you can, as one example, look at the percentage of income coming from interest and capital gains to get a sense for how wealthy and area is.