When I lived in Aruba years ago, it was perfectly safe for women to venture out on their own. In fact, my mother and I did so regularly. Aruba does not (or at least it didn't in the 90s) have the crime and I-hate-Americans problem that many islands do (i.e., St. Croix). I walked aroud the main shopping district with my friends many times, and never had any problems at all. Go ahead and rent there.