I love when I hear from my couples that they've just gotten their marriage license, as I know that it feels so much more real to them at that point! It sure did for me!
In California, you can actually get your marriage license up to 90 days before the wedding. But, since there is no waiting period, you can also get your license right up until the very day of the wedding (although why anyone would add stress like that on that day if they didn't have to, I don't know!).
Unless there is a specific reason for going at a certain point - one out-of-town couple did it on their last site-visit into town two months before the wedding, another went during spring break from school since she is a teacher, and plenty of couples go in the final days whenever they arrive into town - I recommend that you get it around a month or six weeks out. Just so that you aren't worried by doing it relatively last minute. And just so you don't get worried when the reminder arrives in the mail to you after it's been 60 days and your license hasn't been filed you (even though my couples knew that, as they hadn't gotten married yet, it still made them nervous to get that in the mail).
One last tidbit of advice - fill out the application ahead of time, to save you time that day and to be sure that you have all of the information that they ask you for (like parents' state of birth). That's one reason that I send it to all of my couples during our ceremony creation process, and why you can find it here on my website on demand too.
Have fun getting your license, and feeling one HUGE step closer to that day!