PVWatts provides exactly what you're looking for.
It's a solar calculator maintained by the National Renewable Energy Lab of the U.S. Department of Energy. To use the tool:
- Enter the location of the proposed solar system. PVWatts will show you nearby weather stations for the simulation, and uses the most relevant solar irradiation data.
- Enter the system parameters. You can enter either basic info (size, orientation, angle) or provide more detail (inverter efficiency, system losses, etc). You can even draw an outline of your system on the satellite imagery of the proposed location.
The results include monthly solar radiation and AC power production values. If you included your utility rate, it will provide the value of this power as well. You can also download hourly data which includes much more detailed information on irradiance and factors such as temperature and wind speed which affect the output.
PWVatts irradiance data
PVWatts has up-to-date, high-resolution solar irradiance data is for most of North America, the northern half of South America, and the Indian subcontinent. For other parts of the world, older and less precise data sets are used which vary by location. These aren't as accurate as the NREL data, but suitable for rough estimates.
A note on optimal angles
The reason you're getting different answers is probably because the definition of "optimal" for a given location varies according to preference. Are you looking for:
- Any easy-to-remember formula? Install the panels at latitude tilt.
- Greater energy output over the course of the year? Consider laying them a bit flatter.
- Greater power output in the winter? Lay them a bit steeper.
- Less need to clean the panels off? Steeper still.
The topic likely deserves a separate question, but for your purposes playing around with PVWatts will hopefully give you the guidance you need.