Hotel Captain Cook in downtown Anchorage is excellent. There are also a number of chain hotels which are also fine and would qualify as safe.(Obviously when travelling, it always pays to be aware of your surroundings, and use normal caution in even the safest surroundings). There is a lot to see in the Anchorage area, among them: the new Alaskan Native Heritage Museum which we visited last year. If you have time, rent a car and drive down to Portage Glacier and go to the Visitors Center. There is a large seaplane facility and nearby is the Earthquake Park which will give you a good understanding of the Good Friday Earthquake. Enjoy your visit to Anchorage and Alaska. Would go back in a heartbeat.