Aruba is beautiful! :)
I was there about six months before the Natural Bridge collapsed; shame you won't be able to see it. I was only there for a day (it was a port on a cruise), but we spent about 12 hours total on the island.
There's this really cool off-shore island that is run as a snorkel/dive place called DePalm Island, you should check it out if you like water activities. They also run other island tours.
Welcome to De Palm Tours - Your adventure starts here!
My husband and I did the "Sea Trek" which was awesome. It was our second time, and Aruba was much better. It's the location they train all the other people in the Caribbean to do it, so it's huge and you get to see a lot. We've also done "Snuba", though not on Aruba. It's also a lot of fun, much better than snorkeling!
The island isn't huge, and there are taxi drivers all over the place, so you won't have a problem getting around. If you are staying in Oranjestad, you're in luck, there's a ton of stuff to walk to. There are bars, nightclubs, restaurants, casinos, shopping, everything. It reminds me of Florida, actually. The dining can go anywhere from cheap (you can even go to McDonald's) to expensive. We ate at this great place we stumbled upon called Que Pasa. I had the best seafood pasta I think I've ever had in my life. I think dinner for the two of us was about $50 including tip. If that's too high for you, there's lots of other options.
I recommend you go to a local bookstore (like Borders) and pick up an Aruba travel guide. I bought one before our trip, and it was really handy. Frommers and Fodor's both put one out that are great and not too expensive. They reference places to eat, places to stay, things to do, and ball park prices.
Amazon.com: aruba: Books
You can also check out tripadvisor.com, I've given you a link below. There you will find loads of info, as well as stories of people's visits there. It's a great resource.
Search results: aruba - TripAdvisor
I'm assuming you have a place to stay already, but if not, check out this hotel:
Renaissance Aruba Resort & Casino, Oranjestad - Resort Reviews - TripAdvisor
It is simply beautiful, and right in town. There is a ferry which takes you to a private island with a beach in the lobby too! We stopped in there while walking around, and if (when!) we go back, that's where we want to stay. If it's out of your budget, there's a less expensive sister hotel elsewhere on the island.
As far as staying safe goes; Aruba is a really, really safe island. I know the whole Natalie Holloway story gave the island a lot of bad press, but honestly, it's not crime ridden. Use common sense. Get in licensed taxis, don't flash cash and valuables, don't get wasted and hope you make it home OK. Just because it's paradise doesn't mean you can't get hurt!
If you have any other questions, I'm glad to help! Have a great trip!