I'd say it's very possible - depends on where you plan to stay.
Very
much oversimplifying Curacao, there's three main areas:
East Willemsted along the cost where you'll find several resorts: Breezes, Lions Dive and others near the SeaAquarium park/resort area. Most have shore diving and an on-site dive operator for boat diving.
Downtown with minimal/no shore diving but shops/restaurants etc. But there's no real diving in that area due to proximity to the port etc. and I
believe you'd need a ride to one of the nearby dive operations boats.
Further west where there is good diving (imo the best) but most divesites are spread out around 10-15 mins. driving distance from each other. There are a couple of semi-AI resorts in that area, Habitat Curacao and Lodge Kura Hulanda are two, but they're pretty isolated. At LKH you could walk to a couple nearby restaurants in Westpunt, Habitat is on the coast in a housing development so nothing else is nearby. Westpunt is also 45mins. from town so it would be a pricey cab ride. I've been in a suite at LKH, they're pretty nice. It's one of the leading small hotels of the world.
For shore diving, a good option might be the Dive Bus, they offer free pick up at most of the resorts in town and take you diving to some of the better sites both east/west.
The Dive Bus - HOME
They're located adjacent to Breezes slightly east of town. They have a decent shore dive on site also. Suzy/Mark are good people - recommended here often. I've only met Suzy but she was very helpful to us in recommending good dives in their area - due to scheduling she knew we couldn't even dive with them at the time.
Another option for staying might be Piscadera Bay, a resort area slightly west of downtown - the Marriott and Hilton are there among others. The Marriott has an on-site diveop also and the Hilton is one of the Ocean Encounters locations but the reef is farther out there so a longish surface swim. Hilton's reef also has a lot of manmade debris on it so not a great dive. There are a couple of restaurants within walking distance also. About 10mins. by cab from downtown staying in that area. And it's pretty quiet at night. Would be a reasonable cab ride from the airport. The Dive Bus picks up there also.
Or maybe book a package with
Ocean Encounters. They pick up via boat at 3-4 in-town resorts for boat dives and their main facility is adjacent to Lions Dive/SeaAquarium. Afaik, they also have some way (van?) to get you out to their OEWest Westpunt facility to dive some of the better sites out west. If you're interested in the Dolphin Dive, they do it for the SeaAquarium. We booked it directly with Ocean Encounters.
For getting around town, I'm pretty sure the bus system is somewhat reliable. We saw locals using it - IIRC even farther out west. One of the diveops in the Lagun area mentions on their website there's a bus stop nearby.