High adventure is a term that usually refers to activities that are appropriate for older, more experienced Scouts (generally age 13+).
Day hiking is OK.
You are somewhat limited with camping (from the same Guide to Safe Scouting reference that @CharleyHamilton posted above):
These are pack-organized overnight events involving more than one family from a single pack, focused on age-appropriate Cub Scout activities and conducted at council-approved locations (councils use Pack Overnight Campout Site Appraisal Form, No. 430-902). If nonmembers (siblings) participate, the event must be structured accordingly to accommodate them. BSA Health and Safety and Youth Protection policies apply. In most cases, each youth member will be under the supervision of a parent or guardian. In all cases, each youth participant is responsible to a specific adult.
At least one adult on a pack overnighter must have completed Basic Adult Leader Outdoor Orientation (BALOO, No. 34162) to properly understand the importance of program intent, Youth Protection policies, health and safety, site selection, age-appropriate activities, and sufficient adult participation.
Reference: Cub Scout Outdoor Program Guidelines, No. 510-631