Uhm, if of course depends on a lot of things and some more subjective than others. In terms of "The Best Smartphone" right now for under $300USD without any contract - drum roll please - the winner is the Google/LG Nexus 4. It has all the bells and whistles from wireless charging, NFC, Miracast via Android 4.2.1 Jelly Bean brilliant display and a future proof Quad Core processor - at least for 2013. In my hubs I have repeatedly said that one of the reason for getting a Google unlocked phone smartphone is to get the latest OS updates within weeks and while your smartphone is still in fashion ;-)
If you prefer to pay less and get a contract then your choice of smartphones under $200USD is bewildering and very likely depend on what you have in your electronics ecosystem. If you missed it, I'm leaning towards the iOS platform if you already have an Apple ecosystem at home or work. Check out my hubs on more detailed discussion around smartphone choice.