After looking around and reading reviews here, I decided to take my watch to Werner's to have the battery replaced. This was the first time I had done this, but from what I found online, $10-15 is a good price for this service, and the battery itself costs around $6-8 even if I did have the equipment and ability to replace it myself.
I was in and out in under 5 minutes, my watch was fixed and reset to current date/time, and, as the sign said which was posted on the cash register (Watch Repairs $10-18 depending on difficulty) it was $10.
I was very pleasantly surprised and plan to go back next time.