Words for 'escorting,' 'showing around': 带你出去 vs. 护送你出去 vs. 陪你去玩儿 带你出去...
护送你出去...
陪你去玩儿...

I am especially interested in the difference in meaning between the first and third. The third may not be correct because I may be recalling it poorly.
The first seems clear: &quot;...to take you out&quot; in the sense of escorting and showing around. But isn't there a similar meaning for &quot;pei?&quot; The second one is new to me and seems to have a similar meaning.
带 has a sense of lead/host, A带B去 can be used in the situation where B doesn't know the place but A does, so A takes B there and shows him around.

陪 means accompany, it does not have the sense of lead/host. B陪A may be used in a situation where A may feel strange or uncomfortable with acting alone and wants somebody else to accompany him.

护送 means precisely escort, where 护 means 保护 (protect).