Welcome to East Tennessee!!! Since this is on the budget board, let me add a few savings tips as well.
If you are driving around always take Veteran Parkway to get from Sevierville to Pigeon Forge and by pass a lot of traffic. Use the bypass in Gatlinburg if you want to go to the park from Pigeon Forge and you'll save a lot of time and enjoy the beautiful drive as well.
As has been mentioned before, Dollywood is a great Experience and one you will enjoy. Saturday's are the busiest, but the crowds die down around 5:00 pm. Sunday afternoon's are the best time to visit. Best meal for the price is Miss Lillian's Chicken House. The menu ia a rotating buffet of four meats (fried and grilled chicken are always on the menu) while pulled ham, chicken fried steak, BBQ and other options change each day. Also, if you buy the refillable mugs, you get a slight discount if you purchase them with your meal. If you are looking for a great snack, try the cinnamon rolls or cookies at the Old Mill inside the park. If you plan to visit for more than 1 day or come back before 2016, be sure to upgrade to a season pass, super value.
Cade's Cove is a nice drive, but can be very congested. The earlier in the day you go the better, if not, you might be in traffic for a while.
If it's all about Dad, visit the Smoky Mountain Knife Works in Sevierville. It's part store, part museum and at least an hour of looking around. Knives, tools and man stuff.
If you like the outdoor, the best store is NOC located just outside the National Park enterance.
Two easy hike with great site are Laurel Falls and Elkmont.
Someone also mentioned Calhouns, great BBQ. It's not on every Calhouns menu, but they offer a feeds 5 or Feeds 10 take out box at all the Smoky Mt locations and is the perfect picnic to take with you to the mountains. The location in Gatlinburg is right outside the National Park enterance so it's easy to grab one and go to the mountains.
Let me give you three restaurants loved by locals and some tourists, but don't tell anybody, OK....
Best BBQ is at Tony Gore's in Sevierville. It's a hole in the wall restaurant, but has made Southern Livings top BBQ honors in the past. They even offer a buffet on Sunday's from time to time. Great ribs and brisket.
The Peddler in Gatlinburg is a great steak house, but has a nice menu and a salad bar that is the best. My wife loves the trout. The tourist have really caught on to this place, so there is usually a long wait. Trick is call ahead beginning at 4:30 the day of your visit and they'll add your name to the waiting list and estimate your time. Ask for a creek side table, they might accomidate.
Last but not least is Best Italian Restaurant. Here is the real secret, there are two of them. One is located on the middle of Gatlinburg, right in the middle of the shopping and crowds. Don't go to that one. It's the decoy. Only there for the tourist. The locals go to the original, located at the east end of Gatlinburg in the Elks Village. It's another hole in the wall. Decorated in 1970, but the food is great! You have to try the garlic butter rolls.
Hope you have a great time.