Trust the people who manufactured your engine, and use the instructions in the owner's manual. Generally, that means using the oil life gauge.
You know who came up with the "every 3000 miles" charade? The people who want to sell you more oil. I haven't owned a single car that, even under the "severe duty" interval, required it that frequently. But the myth persists. The oil salesmen even helpfully put a sticker on your window telling you when to come back! It's brilliant marketing, but that's all it is. It has no basis in fact. At 3000 miles, you're likely not even close to needing an oil change.
The oil life meter on a modern Honda is not based simply on miles driven, but on a number of factors. It tracks average engine RPM, car speed, miles driven, temperatures, hot and cold starts, and high-RPM events. It takes all that and calculates how worn out the oil is. If you start it every morning and floor it between red lights to work every day like my wife does, it'll have you change the oil in fewer miles than someone who usually just cruises on the highway.
To give you an idea, I do probably 80% highway driving and 20% city, and live in a pretty temperate climate (Seattle). I just checked my records, and I drove a shade over 7000 miles between my last oil change and the one I did last week.
Keep in mind the computer's estimate is for conventional oil. If you're using synthetic, it will last longer than the computer calculates.
Hope that helps.