My wife and I were in Curacao last October for 10 days and with this extended time we were able to see a lot of the island.
We rented a house just a couple hundred yards down the coast from Habitat Curacao which is about 20 minutes outside of Williamsted. As we were outside of town we rented a car for our entire time there. Driving in town was like any other city, outside of town it was a little adventuresome but by the end of our stay I was racing along the back roads just like the locals
Restaurants: For local fare Janchies in Westpunt can't be beat. Do yourself a favor and make the time to visit here. The larger hotels (Marriott, Hilton etc) all had very nice dining. We took advantage of the deli at the Marriott on a number of occasions. If you're looking for some good ol fast food there is a subway and pizza hut in Willemsted on the Punda side. There are a number of Thai and Indonesian restaurants in Curacao. We took a liking to one that was on the Otrabana side of Willemsted called Thai Sawadee. There is also a Mongolian style barbeque in the attached builing. Note that most of the restaurants outside of the larger hotels do not have air conditioning. Thai Sawadee did have A/C.
Attractions: The national park was great for hiking and driving through the hills. Nearby was Boca Tabla where you can visit several areas where the waves violently crash into the shore, one area had a natural bridge although you could not walk out on it like the one in Aruba. The SeaQuarium was OK, the dolphin show was pretty cool.
Beaches: The NW side of the island has many small (and some not so small beaches) with the clearest water I have ever seen. We spent a day just stopping along the beaches along the NW coast. South of town in the Seaquarium beach. Lots of activity here especially on the weekends.
Dive Ops: During this visit I was not yet certified but did do a DSD with Easy Divers at Habitat Curacao (after seeing what was under the water upon return to the states I immediatley started looking into OW classes) Easy Divers seemed like a good operation. I did spend some time at dinner one night at Habitat talking to a number of divers who really liked the place. Near the Seaquarium beach you have your choice of a number of dive ops. Ocean Encounters, Toucan Diving and Lions Dive as well as the dive op at the Seaquarium which was closed when we were there due to construction.
As for peoples attitudes, crime etc. The locals didn't seem to be the friendliest people we have ever met in the Caribbean but we were never treated poorly because we were from the United States and never felt threatened or the least bit uncomfortable outside of the resort areas (driving around, remote beaches, grocery stores, restaurants, gas stations etc.) which is really saying something for most spots in the Caribbean.
One piece of advice would be (for anywhere in the Caribbean) just be prepared to slow down (which is really hard for me) and take things at the islands pace.