I am developing one site where need to display facebook trends by country/city. I search on their API site but i didn't find any api. So is there any API available to grab all trending topics from facebook by country? or any ways to do this things.
You'll need to use the Keyword Insights API, which - as of this writing - is not available. From the link:
Access to the Keyword Insights API is restricted to a limited set of media publishers and usage requires prior approval by Facebook. You cannot apply to use the API at this time.
However, once you're able to get an API key for it, you'd be able to search by city, region and/or country.