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'My family comes from Manchester' is clearer.

Yes, your last statement, 'My family comes from Manchester', is unambigous. My problem is, I don't know how to answer ... lead to the library?' 'The library is next to the bakery.' * Yes and no on a random basis :-D.

I think the best answer to "Are you going to see your family?" (more usual than the "are you travelling" version) is simply to tell the person what you are planning to do. "Yes: I'm going to see my parents", "Yes, I'm going to stay with my sister for the weekend", "No, I'm on business", etc.
I also have a question with regard to what Joe Fineman notes in the other reply. "Are you staying in ... that the two sentences "No, I am staying with family", and "No, I am staying with a family" are equivalent.

OK, this is easy, too. (I hope!)
"I'm staying with family" means you're going to stay with some member or members of your family, but probably not your parents. (I feel this may be a recent importation from America, but I'm not sure.) "I'm staying with my family", almost always means your parents, and implies that a sibling will be there too; if it's just you and your parents, you'd probably say "I'm staying with my parents" as above. "I'm staying with some of my family" would always mean at the house of relatives other than your parents, though one or both of your parents might or might not be there too.
Now that my father is dead, I'd say "I'm staying with my mother."

As a divorced man, I hear my children saying things like "I'll be at my Dad's place till Thursday", and "I'm going over to my mother's house tomorrow."
"I'm staying with *a* family" definitely means that you're going to stay, or are staying, in an ordinary home, not a hotel, with a family you are not related to. You may or may not be paying for it. "I'm staying with friends" means much the same, but tells the listener a little more about the people you're staying with.
Mike.
Yes, your last statement, 'My family comes from Manchester', is unambigous. My problem is, I don't know how to answer questions like, 'Are you traveling to your family?' The answers that I can think of are -

Well, in this case it's just a question of polite interest, so it really doesn't matter much exactly what they mean, or, for that matter, exactly what they understand your reply to mean. But a good way to handle the response, if you care to share the information, is to clarify your exact meaning in your answer. "Are you travelling to your family?...Yes, I will be visiting a third cousin twice removed as I pass through X." Then you can go on to say something like, "That is the main purpose of my trip; to spend the summer with my distant cousin" or "...but I will only be there one day and one night; for the rest of my trip I will be travelling alone."
Or maybe even it's "Yes; I will be reunited with my parents and my brother, after being separated for twelve years while they pursued careers in Europe and I stayed home and launched my business."

It doesn't matter. When someone meets you for the first time and wants to display friendly interest in you, there aren't too many questions he can ask of someone about whom he knows almost nothing. The conversation is like a friendly tennis game: your job is not to hit the ball back to a precise spot, but rather to make a return that your conversational partner can easily return to you. Your job is to make it easy for him to keep the conversation going.

To me, "family" can mean a lot of things depending on context. If I need to be a little more specific, I may say "immediate family" to mean my parents, siblings, children, and spouse; and "extended family" to include all who have any relationship to me by blood or marriage.
I also have a question with regard to what Joe Fineman notes in the other reply. "Are you staying in ... that the two sentences "No, I am staying with family", and "No, I am staying with a family" are equivalent.

Really, "staying with a family" has quite a different meaning that "staying with family." The latter is just another way of saying, "I'm staying with relatives." But make it "a family", and it sounds as if you are staying with a family to which you are not related, but which, either for money or for the stimulus of meeting international travelers, is taking you in as a guest.
Gary Williams
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... My problem is, I don't know how to answer questions like, 'Are you traveling to your family?' The answers ... answer is a bit like - 'Does this road lead to the library?' 'The library is next to the bakery.'

Well, the first thing to be aware of is that here the questioner is almost certainly just trying to make polite conversation, so precision is not necessary. You can be like the politicians, and, rather than trying to puzzle out exactly what the questioner means, you can just answer the question you wish he had asked. Your only real obligation is, as it would be if you were playing some very friendly tennis, to return the serve in a manner that allows the first speaker to easily keep the rally going.Your solution to the understanding problem is to provide enough information in your answer to clarify what you mean by "family". Above all, you must not answer simply, "Yes" or "No"; that ends the conversation. You might say, "I will be seeing my third cousin twice removed when I am in X." Then, if you want to provide more information, you can add, as appropriate, "...but only for a day and a night as I pass through X on my way to Y..." or "...and I will be staying at her home for a month." Or maybe your answer is, "Yes, the main purpose of my trip is to be reunited with my parents and brother, whom I have not seen in the twelve years since they left to pursue interests in Europe while I stayed home to launch my business." Your answer is not, "No." It could be "No; I would not want to draw the attention of the police to them by calling" or "No; I'm afraid I have no relatives within 1,000 miles of here;" or even, "No; all of my family were wiped out by the great mudslide of '01."

Or, if you don't want to talk about your family and your travel plans, then it is up to you to change the topic.
Now, and understanding that it really doesn't matter in the kind of situation you have raised, if I want to ensure clarity when asking the question I use "immediate family" to mean parents, siblings, spouse, and offspring; and "extended family" to mean all relatives.

Gary Williams
And if it's the 'whole family' then there are likely to be cousins of various degrees.

A "family reunion" generally includes all the descendents of some couple along with their spouses, and can involve hundreds of people.

John Varela
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"Are you staying in this hotel?" "No, I am staying ... and "No, I am staying with a family" are equivalent.

"With a family" would mean "as a guest in a private house where a family lives". This definitely excludes, I ... I should still be staying "with family". So the two expressions are not interchangeable, at least in BrE. Alan Jones

Thanks Alan, and all the others who took the time to reply.

I suppose I have much reading to do. I will continue to stick around.

Pradip
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Me, being in US, would use FAMILY for my wife and children. If I were to be in Bangalore, India that would include my parents.

Basu.
Me, being in US, would use FAMILY for my wife and children. If I were to be in Bangalore, India that would include my parents. Basu.

Basu, the usage is "in the US". But family is family when I refer to my family, I include all family members who are here in the US, in Bharat and several other countries. A parivaar is a parivaar.

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