Ahoj,
With 10 and 13 year olds, take the Diana Funicular to the observation tower. There is a minor petting zoo at the top and the tower has great views. Hike down arriving back by the GrandHotel Pupp for a slice of Pupp cake in the cafe. Explore the halls of this grand dame of hotels and read up on former guests such as Goethe, Bach, Beethoven as well as modern day whos who.
Then catch a city bus or rent electric bikes for an excursion to the town of Loket. Often used in films, including as a stand in for Montenegro in the James Bond filmed at the GrandHotel Pupp, it’s picture perfect. It has one of the most approachable medieval castles dead center in town with a wild dragon at the castles heart. Not to mention the notoriety of having a meteor land dead center in its courtyard that drew observers for years. There is a dungeon that has some gory so might want to pop through first before sending the pups through.
If rain is a concern, book a hotel with natural mineral springs pumped in for a pool day. I’d highly recommend the GrandHotel Pupp with their crazy, huge, stainless steel mineral baths pools and maze of saunas, ham mans and salt caves that make for spa heaven. Prices can be surprisingly affordable.
Eat at Pizzeria Asti. The pizza is solid and live music on the weekends is fun.
That’s my two cents.