I know nothing about kayaking so take this for what it's worth.
We dove Playa Kalki, off Westpunt on the far west end. All West Apt's is there - a lot of divers stay there since there's a diveshop on site and the beach is just down (a lot) of stairs. Local fishermen work off the pier there and on the far west (seems like north) end of the bay people kayak along the cliffs under the Lodge Kura Hulanda.
Westpunt is about 45mins. from town and very quiet at night. If you were to stay out there, you want to arrange flights so you could stop at Centrum or Cost-U-Less for food before driving out - both near the airport.
Another option could be Playa Lagun, nice beach, it's a sheltered cove leading out to deeper water. Also fishermen there. There's about 2-3 condo properties surround ing it, Lagoon Blou, Bahia Apts. and one I forget, 2 restaurants and about a 30min. drive to town. Lagun is a weekend area for residents so there's also some small rental properties but although they're waterfront - it's about 60' down. You'd have to drive the kayak down the street to the beach at Playa. We stayed at My Dreams apts. I'm reasonably sure my 1 br with full appliances - except no oven - was $60/nt. My deck was water front - 1/2 the units face the ocean, the others the mountains and they have bbq facilities. It's also very secure - high wall, locked gate, bars on the windows. Typical in Curacao in some areas. From there a few blocks north is Playa Jeremi - another nice beach entry. It would be good with the kayak since there's big stone slabs leading down to the water from the parking area. No facilities there at all though.
I think Varsenbaai might be another good spot. It's a beach with a small dock, has an on-site dive operation, restaurant and is a locals beach. No accommodations off the beach though.
Another would be Porto Mari - it's pretty calm being fronted by a double reef, nice beach, snackshop, locals will fill the parking lot on weekends.
I would think, but do not know that there would be good kayaking around Blue Baai also just north of town. From there you could paddle around into Piscadera Bay as well. Even beach at Pirate's Bay beach bar for lunch. We ate there a couple times and I might've seen a kayak there once. P-Bay is not very busy but there is the occasional boat. We stay at Piscadera Beach Resort - condos on the upper end of your budget but they're across the street and up the hill from the water. It's a convenient area, nearby food, 5mins. from downtown.
Pierbaai Beach slightly south of town would be easy with a kayak also. We go to a restaurant there and the water is 50' from the parking lot.
Really most of Curacao's west side is pretty calm. As divers we look for currents to drift dive, about the only ones we found were west of Westpunt or at a site called Lost Anchor mid-island.
Also along the south side of Willemstad in front of many of the resorts there's a rock breakwater. As divers it's in the way but it makes for a calm lagoon/beach. Look at pictures from the Avila hotel website - it's out front there and extends south afaik. Sites 20-22 in the link below show parts of it.
Avila has a great jazz club some nights but it's smoky.
A lot of Curacao's west side is high cliffs overlooking the ocean with breaks for beaches. Seems like it would all be good kayaking except you wouldn't be able to get out in some areas as the cliffs are 50-60' overhead.
Can't help with the fishing, I don't eat what I go to see.
I don't know the area you mentioned, but I recall seeing kayakers in the distance once off Caracasbaai south of town.
Really just about any beach on Curacao has some sort of facilities - often a dive shop with food, lockers, showers, etc. You can see pictures of a lot of them here -
Scuba Shore Diving Site Listing for: Curacao, ABC Islands
One area to probably avoid in the kayak is south Piscadera near the north side of Willemstad harbor as the cruise ship megaport is there. We can't even dive a wreck nearby when the ships are in. Also the port itself is a working container ship port as well as busy with shuttle boats from the cruise pier to the old downtown.
