Born and living in this district, I'm obliged to know in detail its touristy destinations and... the other. Alcobaça, Batalha and Óbidos are the top destinations, closely followed by Nazaré, Leiria and Caldas da Rainha. However, many other places may be added for all tastes:
Beaches, from the popular São Martinho do Porto, Foz do Arelho, Baleal or São Pedro de Moel to the less known Consolação, Salir do Porto, Paredes da Vitória, Água de Madeiros, Vieira de Leiria or Pedrógão Grande, here and there with many nice wild beaches (Falca, Vale Furado, Légua, Polvoeira, Salgado, and more).
Peniche, with a wide beach and good fish is the launching harbor to Berlengas.
Inland, Porto de Mós, Ourém are also touristy, with natural life boosting in the Natural Park of Aire and Candeeiros mountains, accessible from many villages (Turquel, Évora, Benedita, Arrimal, Mendiga and more).
Some other small places, here and there, may "hide" a special restaurant (Ataíja, Azoia, Tornada), a monument (as Cós), a club (Pousos), a spring (Chiqueda), a performing group, a pastry (Alfeizerão), but mainly, a naturally welcoming people (Gaeiras).