Many times it has occurred with me that,the place I am visiting doesn't know about my eating habits & they take efforts & prepare unsattivic food.I am in dilemma as how to refuse the food provided by them without hurting their feelings? 

just tell them that it is good to Your spiritual and healthy life. Who told You that eating onion and garlic we can enjoy life??? These foods are in the mode of ignorance. And when we eat them they make our brain ignorant. Because all living entities have their own qualities. Even plants. When we eat them we will get their qualities. As like with whom we associate we get their qualities.

How many life times we will try to not hurt someone???? It will happen. But at least in this life time we have to please our Supreme Father Krishna. And Krishna is like root. When we take care of the root nicely then the whole tree will flourish. If Krishna is pleased with You then all Your relatives also will be automatically pleased.

If one becomes a pure Devotee Krishna promises that all beloved ones of that Devotee also will be saved from the cycle of birth and death.

So why loose time for eating onion and garlic?????????????????????

On the contrary preach to them that they also should not eat if they want to be healthy. On the place of those products You can use hing it is a spice.