Here are some delightful day out options in Hertfordshire, a county in the south-east of England:

1. Day out in Saint Albans:
- Explore the ancient sites and rich history of Saint Albans. Visit the St. Albans Cathedral, one of the oldest sites in Hertfordshire and a sight to behold. With free entry and free guided tours, you can see the million-year-old architecture and mesmerizing medieval art on the walls. The Verulamium Park and Museum is a must-visit, located near the Cathedral. The museum is filled with remarkable artifacts and ancient treasures, depicting the past life of the Romans. After the museum, enjoy the park – 100 acres of lush greenery with a lovely lake, play areas, a cafe, and wildlife. Take a stroll around the lake, enjoying the trees and meadows full of wildlife and water birds. It's great for a relaxing Hertfordshire day out. Also, if you're into theater, visit the 2nd-century Roman theater directly outside the museum.

2. Warner Bros. Studio Tour London - The Making of Harry Potter:
- The Warner Bros. Studio Tour is the most popular day out in Hertfordshire. Here, you can see some of the sets from the Harry Potter series, drink a butterbeer, and go on a tour. This is an absolute must-visit place for fans of Harry Potter. Explore the authentic Harry Potter film set, with behind-the-scenes previews. You can also take a tour and enjoy the exhibits, adding a touch of magic to your trip. Located in Leavesden, this is the highest-rated attraction in the world. Spending a full day here is highly recommended!

3. Paradise Wildlife Park:
- Hertfordshire's Paradise Wildlife Park is one of the most interactive zoos in England, with an enormous collection of 800+ animals. Encounter various big cats (tigers, leopards, etc.), penguins, wolves, reptiles, meerkats, and lemurs. It's a great family-friendly attraction for animal lovers.

4. Berkhamsted Castle:
- Explore the ruins of Berkhamsted Castle, a historic Norman motte-and-bailey castle. Learn about its fascinating past and enjoy the scenic views from the castle mound. It's a great spot for history enthusiasts and picnics.

5. Ashridge Estate:
- Discover the Ashridge Estate, a National Trust property near Berkhamsted. Enjoy picturesque woodlands, rolling hills, and ancient trees. The estate offers walking trails, wildlife spotting, and stunning views. It's perfect for nature lovers and outdoor enthusiasts.

6. Hatfield House:
- Visit Hatfield House, a Jacobean mansion with beautiful gardens. Explore the historic rooms, admire the art collection, and stroll through the formal gardens. Don't miss the famous knot garden and the peaceful water features.

7. Knebworth House and Gardens:
- Explore Knebworth House, a Tudor Gothic-style mansion near Stevenage. Discover its rich history, beautiful interiors, and extensive gardens. The dinosaur trail and adventure playground make it a hit with families.

8. Hitchin Lavender:
- During the summer, visit Hitchin Lavender and immerse yourself in fragrant lavender fields. Enjoy picking your own lavender, taking photos, and relaxing in the serene surroundings.

Remember, Hertfordshire offers a mix of history, magic, wildlife, and natural beauty – perfect for an unforgettable day out!