The definitive beachfront hotel in CT is The Bay Hotel in Camps Bay, but that doesn't help OP.
First week in January is fiercely busy, so take what you can get. Having said that, Hout Bay, nooooooooooooooo. Nice views, bit of a dump. Fine if you have a car; without one, it will get stale quickly.
I would investigate Bantry Bay; well located, great sea views, you don't need a car...walk to Sea Point or Clifton...and a couple of 4*s and decent guesthouses to choose from.