As of Jan 2011, Andong has a new bright and shiny bus station which is much nearer the freeway and not close to the train station anymore. Buses #1 and #2 go to the train station, and take about 20-30 minutes, 1200 won.
I tried to get a bus from Gyeongju to Andong, and they were sold out for the day because the originate elsewhere and so Andong had no tickets to sell. I had to buy a ticket to Daegu (Dongdaegu) and get one to Andong from there (they leave almost every 15 minutes). That was very doable, but you did have to cross the road in Daegu and turn the corner to get to the building where the Andong buses leave from.
I did not see any lockers at Andong station, however, if you are visiting Hahoemauel (Hahoe folk village), they have a set up for left luggage at the second information center (not the one near where you buy your ticket, but after you take the shuttle to the entrance to the village). You sign it in and they give you a tag.
Also bus #46 to Hahoemauel is still catchable opposite the train station, and it also stops on the main road outside the new bus station, so if you want to return to the new bus station after visiting the village, you don't have to go downtown first. The bus to the village takes about 40 minutes and is 1200 won (as of March 14, 2011).
Another tip, if you are going from Andong to Gangnam (Seoul Central City bus station), you have to be able to enter a PIN to use your credit card, and it wouldn't accept the PIN I used to get cash out. I didn't have enough cash, so was figuring I had to go to Dongseoul station instead which doesn't require a PIN, when this 28 yr old guy helping me out with English bought my ticket without my even knowing. After much pressing, he took the 8000 won I did have, but wouldn't accept any more when we got to Gangnam and I could access an ATM. That is just one of many of stories about how helpful and above and beyond the Koreans have been to me as I have traveled independently through the country. There may not be much English, but the ones who do go way out of their way to help you.