How to Mention Relocation in Your Cover Letter
You will typically benefit from directly addressing the fact that you are moving in your cover letters. This will make it clear that you are not applying just as a way to get to the new location. Your main rationale for applying for any job should be the nature of the work, followed by the appeal of the organization. So, a statement that addresses your interest in the job should precede any reference to the fact that you're relocating.
This type of statement is typically included early in the first paragraph of a cover letter. For example, you might say "I am highly interested in consideration for the associate position since it would enable me to apply my project management skills and also would tap my passion for event planning. The recent trajectory of growth at Maximum Communications, including the addition of Pepsina as a client, further stimulated my interest in applying. My wife and I are planning to relocate (or are in the process of relocating) to the Seattle area to be closer to her family, so the timing is ideal."
Another way to address relocation is to incorporate a statement in a final paragraph which mentions traveling to the area. This makes it clear that the employer wouldn't be responsible for travel costs or any other expenses.
For senior and hard to fill positions, organizations usually expect to fund travel and bring in candidates from outside locations.
However, for more entry level jobs there may be a preference for local candidates. You could say something in your last paragraph like "I would welcome the opportunity to meet with you to discuss this position. I will be traveling to Seattle for a conference (or to find an apartment or to network with local college alumni) in two weeks and would be available to meet at that time. I would also be glad to travel for an interview at your convenience."