General
Aruba is known to be safe with a very low crime rate. However, you should still use common sense and be alert outside of the tourist areas or Oranjestad. As credit cards are widely accepted, it should not be necessary to carry large amounts of cash, just some small bills for cab fare and general tipping.
The second largest city in Aruba, San Nicolas is a modern development that rose with the island's oil boom. The area has a typical British Caribbean heritage. You will also find nice restaurants in and near San Nicholas, and while primarily Aruban oriented, do work to make tourists feel welcome. They usually have some English speaking waitstaff and will explain the native dishes to you.
Other Neighborhoods
For the most part, the other neighborhoods of Aruba are native housing and shopping. The major exception is Noord, which is really an extension of the high-rise area. If you pick a restaurant from the guide books or local English tourist newspapers, you will most likely wind up in Noord at least once -- whether you realize it or not.