Käsmu, set on a rocky shoreline, has plenty of low-key guesthouses. If you want rowdier beach action, head to Võsu, a popular summertime hang-out for Estonian students. Guesthouses are scattered throughout the region; the visitor centre in Palmse keeps lists of options. It's worth keeping in mind that lots of small guesthouses have dogs (big ones). Keep that in mind before vaulting over fences.
The camping is fantastic in Lahemaa, with lots of free, basic RMK-administered camp sites. You will find them near Tsitre at Kolga Bay, at the northern tip of Juminda and Pärispea Peninsulas, immediately south of Võsu and by the Sagadi–Altja road, 300m south of the Oandu trail. When looking for these sites, keep your eyes peeled for the small wooden signs with the letters ‘RMK’. All camp sites (free RMK ones and private ones) are marked on the excellent Lahemaa Rahvuspark map available in the visitor centre (€1.90).