I'm afraid of telling people that I don't eat meat, what do I do?

If they don't like your decision, then that's too bad for them, isn't it? You are doing this for yourself. If you have a conviction, a sincerely held belief, or conscientious scruples against eating the flesh of dead animals, you shouldn't have to compromise your values - nor force them onto others. You will find vegetarian options at nearly EVERY restaurant - that is a non-issue. (It can be trickier for a vegan, but certainly manageable). If you're not critical of their eating habits, then why should they be?