Actually, a very useful tool is available for the iPhone. The app creates setup files for the mic to compensate for flaws with the iPhone mic. I have this device for audio testing:
iAudioInterface2
There are multiple modules within the app that are in app purchases. I have purchased most of them. The developer of the software is very good. There are a few SPL meter options within the app. It's a good dirty test that is pretty accurate and almost always on me. The full test rig is only used when tuning an audio system.
Any cheap ones will be no better than an iPhone with the built in microphone. Any good meter worth buying will have a calibrator available to set reference level. I have the calibrator for the microphones I use :
Calibrator
Microphone Set
I'm not saying you would need these, but be aware that there are different levels and standards when it comes to measuring audio and the accuracy required.
Other testing is being required for some systems. One such test is meeting STI standards. This quick search pulled up this information
I also do have an older Tenma 72-860a with a calibrator.
For the testing you are planning on doing, use the AudioTools with the SPL module if you have an iPhone.