Can someone suggest me a working 16x2 3v3 LCD to work with FIO.
I don't know what a FIO is but, if volts are the problem, you might consider ditching the 16x2 idea and using a Nokia 5110. They made to run on 3v3, are dirt cheap, and have more useful display than any 16x2.
I have standardised on them and find them even more useful than a 20x4 - not to mention cheaper.
Note that I am disappointed with the one with a blue background light. The light is useless and it is better left disconnected. The others are white and are fine.