We loved Aruba! It felt very safe and I was not at all concerned about touring Oranjestad with just my son and I. Our only complaint was that our ship only docked for 5 hours, so we weren't comfortable going to far from the ship.
There was a bird sanctuary, emerald diamond exhibit and shopping area right at the ship yard. As well as tables and chairs under a tent that you could get wi-fi. $3 for 1 hour, $5 for 2 hours. Although - beware - there is a resident iguana sauntering around! He wasn't dangerous - but he walked right under our table and was sniffing my son's toes before we realized he was there! We mailed a post card from the shop at the port - and it cost $4 for the postage. There were lots of tours/excursions with the cruise line. However, if you were interested, there were several passengers trying to gather groups together to negotiate a tour with a local guide. If you are looking for something a little different, there is a not-for-profit group called Friends for Colombia (dot org) that will pick you up and take you for a wonderful tour. We did not do this because of a personal issue, but have been in contact with others who've done it and enjoyed it very much!