How do I say 'You are welcome to come with me' in Japanese?
If I am travelling and I want to invite someone, how can I say 'You are welcome to come with me'?

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Answer

I feel a straightforward translation would not be natural.. 
In japanese if you want to ask someone, you should say
  "一緒に旅行へ行きませんか？"  Shall we go to travel?
  "もし良かったら一緒に行きませんか？"  Could you come with me if you want?
On the other hand if your friend ask you, you could say
  "大歓迎です"  You are very welcome

Answer

一緒に来てくれたら、大歓迎です。

or 一緒に来てくれたら、うれしいです。
This is a kind of suggestion to ask the person to come with you.
But it's more natural in Japanese.

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If you want to invite someone to go with you, you can say 一緒（いっしょ）に　旅行（りょこう）に　行きませんか（いきませんか）。

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В Россию путешествуй...в японии взрывается все) топит их

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あなたは旅行に私と一緒に行くことができます