Walk around the promenade: possible but very unlikely: promenades are long and narrow, and built for walking along.
Walk along the sand: fine
Walk along the beach: fine
Go along the seaside: It's not clear what this means. 'Seaside' is actually a very general term for quite a big area, including the town/resort (equivalent ro 'countryside') ,so along doesn't fit.
Go along the coast: fine
Sail on the sea: fine
Sail around the sea: This is unclear. You could sail around/round a lake, meaning round its edges - but sail around the sea doesn't mean anything. You could perhaps say 'sail around on the sea', if you were sailing about on the sea but not going in any particular direction.
Sail across the ocean: fine