Does anyone have a suggested simple project using the Arduino Uno and the microtivity LCD Module 1602?
Not really. LCD displays are usually used to show you data or debugging information about other hardware. They're not much use without something else providing information for them to display. To start with, wire it up and make sure you can send text to it, master moving the cursor, clearing the display, doing periodic updates using millis. If you have some switches, you could implement some menus.