Grammar usage(Use of Capatilization)

Sanjay, I found this guide online that answers your questions.  I agree with the rules spelled out there.

http://www.proofreadnow.com/blog/bid/30440/North-East-South-or-West-Capitalize-or-Not

However, there are a number of other grammatical mistakes in your example sentences.  Please see my corrections below.

They are going to flavour southern cooking.  As the online guide says, southern should be capitalized when referring to regional cultural activities.  Also, if they are going to flavour Southern cooking, it means that they are going to add some spices or other ingredients to the food.  That is not what you mean, I don't think.   You are talking about eating and enjoying Southern cooking.  They are going to enjoy (some) Southern cooking.

 The eastern of the yellow stone park is in wyoming. Yellowstone is one word, not two. Eastern is an adjective, so that word does not go with a prepositional phrase like of the Yellowstone Park.  You are confused between adjectives like eastern and their complementary phrases, common in British English, the east of + noun.  It is not common to talk about the areas of a park using either expression; instead, for a smaller area, like a park, we would tend to say the east (or the eastern) part of.  Also, you don't need the with the name of a park.  The east(ern) part of Yellowstone Park is in Wyoming.  I should also point out that there is a superlative form of the adjective eastern: easternmost.  So you could say The easternmost part of...

The northern of new england states are a great place to see fall colors. Again, an adjective like northern does not collocate with a preposition phrase.  You need the adjective (not the corresponding the north of construction) because states is a countable noun.   The northern New England states are a great place to see fall colors.  Some might argue that you should change place to places but I think these states can grammatically be considered a place in this context.

I hope this helps.