Address the person by name in the salutation, and be certain that you have correctly spelled it.
Open with a mention of how you know the person just moved into in the neighborhood, joined the staff or whatever setting is relevant. This will put the reader's mind at ease about getting a letter from a stranger.
Pay a compliment if possible, but nothing too personal. For example you might mention that you think the house they just bought is cute. If the person is a new colleague, mention something complimentary that you've heard, perhaps that "the boss says you're a dynamo."
Offer help. Make yourself available to show a new resident the closest shopping centers, or offer to show a new colleague around the building. Be specific so your offer will sound more sincere, and the recipient may be more likely to take you up on it.
Mention any important dates, such as a neighborhood yard sale. In the workplace, you might mention that people from your department like to have lunch together on Fridays or something similar. Include a list of helpful information such as trash day and so forth.
Close with one sentence that says "welcome" in some way. When you sign off, it's a good idea to add your email, phone number or extension.