I'd say "going to the beach". I've never heard "going to the sea" but "going to the seaside" is fairly common, though probably a little old-fashioned. For me "seaside" has images of old fashioned seaside holidays and sticks of rock and candy floss and fish and chips on the pier.
Also, I've seen the words "beachfront" and "ocean" used in fanfics. Avoid them.
I'm not certain what a beachfront is, it seems to mean both seaside and promenade (or prom). I'm a 15 minute cycle ride from the beach, and the prom. I'm very close, but nowhere in the UK is further than 70 miles from the sea.
Ocean isn't used because we are surrounded by seas, not oceans (except for north west Scotland and (I think) Cornwall).