What is best [under $200] blue ray player with all area code free?

I would try some of those Canal Street type of retailers like B&H. They sell cheap and usually have a good selection of gray market products. Check Amazon as well.

I have an LG BD330 Blu-Ray player that works extremely well for me. It is not sold region free, however, there is a very simple hack you can do to make it region free. Alternatively, I also use an OPPO 105 that works extremely well on just about any format. I use an outboard hardware hack (purchased on eBay for $70) that converts it to region free (DVD) and zone free (Blu-Ray). Region free DVD playback is automatic, zone free Blu-Ray playback is not (you have to program it for the required zone, simple set of commands on the remote).