1 Day is doable.. but not a lot of sightseeing..
From HB to Fremont via 101 looks like around 550 miles. As a rule of thumb, that's going to take you about 10 hours driving time with minimal stops (getting gas, having lunch, bio breaks). That's about 100 -150 miles farther than taking the I-5 route up, so you do need to factor in the extra time just to cover the distance.
It's doable in a day -- I've driven it several times. But you're not going to be doing much sightseeing, other than out the window of the car. You *can* do the coast route up through Big Sur from Morro Bay to Monterey, but that's going to probably be the slowest part of the trip in miles/ hour (but very scenic) which means few stops if any.
If you get a really early start out of HB (say hitting the road at 6 am) you might be able to add in some fun times to do things -- say the tour at Hearst Castle (figure at least 90 minutes, and probably 2 hours), or walking on the wharf at Monterey etc. And if you're doing it in a day, if you're not heartset on visiting Santa Cruz and running tight on time, I'd definitely take the Castroville - Prunedale connection to get from Coast Highway back to 101. Santa Cruz is a great town, and the boardwalk is fun to visit -- but I think you'll be short on time at this point.
Fremont WA or Fremont CA?
I'm just a tad confused because you say you're going to Seattle WA and there is a wonderful neighborhood in Seattle called Fremont. Obviously you didn't mean the Seattle-area Fremont but you still have to get to Seattle right? If you have another 2-3 days for this leg of your trip, definitely take 101 up the coast from Fremont, CA, to get to the Seattle area.
Depending on time, there are numerous places you could go inland to I-5.
* At Astoria, OR, go east on Hwy 30 to the bridge on 432/433to go through Longview/Kelso to I-5
* Take the really fun-to-drive Astoria Bridge over the Columbia River to Hwy 4 through Longview/Kelso to I-5....I think this drive is a tad prettier than the one above but they are both nice drives. I think the AStoria Bridge is so cool that I would drive over it and turn around and come back to Astoria if you decide to take take Hwy 30 to I-5 (see above).
* If you continue on 101 into Washington, you might also go east at Raymond to I-5 on Hwy 6. Or go north from Raymond almost to Aberdeen and take the 107 spur to Hwy 12/8 into Olympia and catch I-5 there.
* If time is not a factor, I would encourage you to take 101 all the way around the Olympic Peninsula before going into Seattle. It's a gorgeous drive and takes you to some more remote, wild areas of the Pacific Coast and you can visit part of Olympic National Park's unique rainforest. If that interests you, there are numerous ways to get from the Olympia Peninsula to Seattle area. Here are your options (basically north to south...all ferry options except if marked "non-ferry"):
(1) Just east of Sequim, go north on Hwy 20 to the beautiful Victorian town of Port Townsend, take the Port Townsend-Keystone ferry to Keystone, then you can either:
(a) Go north on Hwy 20 to meet up with I-5 near Mt. Vernon, then south to Seattle; or
(b) Go south on Hwy 525 to Clinton and take the Clinton-Mukilteo ferry to the north Seattle area and catch I-5 South into Seattle; or
(2) Just east of Sequim, take Hwy 104 across the bridge, and...
(a) Continue on 104 to Kingston and take the Kingston-Edmonds ferry to Edmonds, then drive south a tad into Seattle.
(b) Then go south on Hwy 3 and then east on Hwy 305 through Poulsbo (one of my favorite towns and worth a stop) and then onto Winslow where you can take the ferry into downtown Seattle (this is where those famous photos of Seattle's skyline are normally taken from)
(c) Then go south on Hwy 3 to Bremerton. Bremerton has a great water tour of mothballed and current US Navy fleet that's fun to do. Then take the Bremerton-Seattle ferry. This docks at the same location as the Winslow-Seattle ferry and gives you the same views of Seattle on your approach.
(d) Then continue south on Hwy 3 past Bremerton to Hwy 16, then Hwy 160 to Southworth and then take the ferry to Fauntleroy, then drive north to Seattle
(e) Non-Ferry option: Then continue south on Hwy 3 past Bremerton to Hwy 16, then stay on 16 into Tacoma to I-5 and then drive north to Seattle from there. You will be crossing the new Tacoma Narrows Bridge which is the second replacement since Galloping Gertie...if you haven't seen the footage, you might google for it. It was amazing. The old, old bridge bucked like a bronco during a storm and collapsed.
(3) If you really want to enjoy riding the ferries, you could go into Tacoma and then take the Point Defiance-Tahlequah ferry onto Vashon Island, and then drive to the north point of Vashon and take the Vashon-Fauntleroy ferry, then drive north to Seattle.
(4) Non-Ferry Option: Take Hwy 101 all the way around "the loop" around Olympic Peninsula ending up going through Shelton to hook up with I-5 at Olympia, then north on I-5 from there.
Check out the Washington State Ferries website for sailing times, fees, etc.
There is no best place to cross-over. Each has charming towns, beautiful landscapes and views of the water. If you want more information on some of these options, just post here and I'm sure several of us can fill you in.
1 day trip from HB to....
If he's set aside 1 day to go north on the coast route from Huntington Beach, CA it's got to be Fremont CA. No possible way to go from HB to Seattle area in a day via the coast route.