If you are flying in and out of LA I certainly wouldn’t recommend trying to see both coasts of America in 2 weeks. As mentioned, it’s a 6 hour flight from LA to NY which means you’ll effectively waste 2 days in the crappiest airports in the country.
Since it will be the middle of the summer and you’re willing to entertain some driving I’d recommend:
Land in LA, and take R66 and head to Vegas. There are some very old and interesting (if not depressing) sites of old America along the way which might be interesting, and it will help your jetlag since you can stay up all night and party in Vegas. During the day it will be too damn hot to do anything besides sit by a pool, but you can make a trip out to see the Grand Canyon.
From there you can head north to Lake Tahoe which is beautiful (and breaks up the trip) then head up to Portland. Portland IMO you could probably get a pretty good taste of in about 2 days. It’s a very small walkable city and any events going on will give you a good fill of weird.
From there I’d suggest heading down and picking up RT 1 along the coast - beautiful twisting views of the Pacific (hence the convertible. Also because we drive on the right side of the road, driving south means you’ll get the best view).
From there you can hit up any number of sites in CA. Napa wine country, SF, and LA all have a lot to do. If you migrate down the coast that way you should be able to break up your trip in a couple day chunks with plenty left to see.