If you take a right out of the plant, next to the building is a small photo opportunity - a sign reading "Dr. Pepper, Texas" It's a nice little way to have a memory of your trip to Dublin.
The number one thing to do is to take a tour of the plant! You start off the tour with a 6oz. bottle of the famous cane sugar based drink, then you get to see the bottling line, shipping area, and a small museum. The tour itself is modestly priced ($2.00 for adults) and ends in a soda shop where you can buy food, souvieners, and even some cans to go. Be sure to check the website for tour times, because there is a farily long break for lunch where you'll have to kill some time if your arrival is off...
Inside the plant, you have a soda shop which serves sandwiches, soup, and of course, their Dr. Pepper. Dining options in Dublin were very limited when we visited, so we ended up eating here. Prices are fairly cheap $3-4 for a sandwich, and $1-2 for a Dr. Pepper depending on the size you order. The sandwiches are standard Deli-type, and made to order. There are a few tables available in the gift shop area for you to enjoy your food at.
Favorite Dish: I recommend the chicken salad if it's available. And of course, order the Dr. Pepper.