Three days to travel all 363-miles of the Oregon Coast would limit your stops to only the most accessible attractions and leave little time for hiking, long beach walks or to feel like you have really experienced the coast. It’s possible, but you would pretty much be limited to short stops, getting out of the car for views, then continuing on your way. I usually recommend a minimum of 5-7 days to include the stops you mentioned.
As for towns to stay in, a night in Brookings or Gold Beach offers you the opportunity to make a few stops in the Samuel H. Boardman State Scenic Corridor and Cape Sebastian. The Boardman corridor offers a few easy and rewarding stops including Whaleshead Beach, Arch Rock Viewpoint and Natural Bridges, but some of the best experiences are short hikes away. My favorite short hike is to Thunder Rock Cove and then continuing to Secret Beach (Miner’s Creek). Cape Sebastian is either a five minute stop for a couple of viewpoints or a few hours on the great trail. Nearby Meyers Beach is a great one to enjoy a long beach walk.
I would plan your next night (or two) in Bandon with stops at Port Orford and Cape Blanco along the way. Port Orford can be a quick stop at the Battle Rock viewpoint or you can visit the small, but unique port for an authentic Oregon Coast experience and spend an hour or two on the short trails at Port Orford Heads. Cape Blanco will likely be a stop just to visit the lighthouse, though there are some trails and beaches there too. You will want a full day for Bandon including the amazing beach and viewpoints of Face Rock and Coquille Point. The Old Town is worth a visit, along with its short riverfront boardwalk. I would make Cape Arago a day trip on a second day. Take some time at the three State Parks. There are majestic wonders to be seen and rushing would be a shame. In May, you should see seals with pups if you walk along the trails either direction from Shore Acres. I’d make this one of your places to linger and hike, then return to Bandon, hopefully for a sunset on the beautiful beach which is hard to get enough of.
I would make your next stop the town of Yachats, but you will need to plan time on your travel day for at least an easy stop in the Oregon Dunes (Oregon Dunes Day Use Area or Honeyman State Park), Florence‘s nice little Old Town, Sea Lion Caves and the Heceta Head Lighthouse (a short, but shouldn’t be missed hike). You’ll pass through the Cape Perpetua Scenic Area just before reaching Yachats and if you’re out of daylight, it’s okay because you will want to come back in the morning and spend some time in this area. Hiking between Cook’s Chasm and Devil’s Churn offers views of a truly breathtaking part of the Oregon Coast. Yachats itself has a nice oceanfront trail, great for a morning or evening stroll. Two nights in Yachats would offer you a great experience, perhaps with part of a day devoted to Seal Rock where great overlooks and the short, but scenic beach are the highlights.
On your next travel day, you will want to make time for Newport area attractions including Yaquina Head Outstanding Natural Area, the historic bay front and the nearby Devil’s Punchbowl, the Otter Crest State Scenic Viewpoint at Cape Foulweather and perhaps a stop at Depoe Bay for whale watching and the unique little town. Newport makes a convenient overnight with lots of lodging options. If you check all of those things off your list, I’d set sights on Cannon Beach for a day or two. Along the way, you might want to make a short stop at Neskowin for the short walk to the beach at Proposal Rock, then continue on to the Three Capes Scenic Route. Cape Kiwanda can be a short stop, though if you trudge up the giant sand dune the views become even more impressive. Cape Lookout is best if you have time to hike or linger on its beach, but I’d save the majority of time for Cape Meares and the short walk to the lighthouse that loops the cape.
On your way to Cannon Beach, you’ll pass through Oswald West State Park, but it’s easy to double back if you spend a night or two there. Oswald West has highway-side viewpoints on Neahkahnie Mountain that can be a short stop, but the park is best if you have time to hike. There’s a short walk to Short Sand Beach that is worthwhile and the Cape Falcon Trail is great for a longer hike. In Cannon Beach, you will want time for the beach and Haystack Rock and Ecola State Park that is worth half a day or more if you want more hiking, but the easy views are pretty amazing too. Staying an extra night in Cannon Beach would offer the opportunity to visit Hug Point or stretches of the beach north and south of the often busy beach at Haystack Rock. It’s also easy to do day trips to Seaside or Astoria from Cannon Beach and the town is fun to explore.
So, I hope this helps and that you have the flexibility to slow down and really enjoy the Oregon Coast. You have a long list of amazing places to see, but three days is too short to do them justice.