Many of the Trek stars' stars are right by there: William Shatner is at 6901, in front of Mann's Chinese Theater; DeForest Kelley is right next to Doohan's; and Patrick Stewart's (interestingly, his only one so far is for live theater) is also at 7021. Leonard Nimoy, Nichelle Nichols, Gene Roddenberry, and George Takei are all a few blocks away, at 6651, 6681, 6683, and 6633. I was mildly surprised to discover that Walter Koenig doesn't have one.
I didn't know how one gets a star, but it turns out to be about as I'd expect: the person is nominated, a committee selects, and then the star is added - after the person nominating them comes up with a $15K fee. The only requirements are that the nominee must have been in the business for at least five years, and if alive, must be present at the unveiling ceremony. The latter requirement causes problems for some older nominees, and in fact Doohan's ceremony is expected to be his last public appearance, as he's fighting Alzheimer's, diabetes, and fibrosis of the lungs. I'm happy they were able to do it while he was alive.