The ones that are strange to me are "Walk around the promenade" - 'walk along' would be more obvious, because a promenade is thin and narrow. "Go along the seaside" - because the seaside isn't a particular place, it's a more abstract idea of 'places near the sea'. "Sail around the sea" - because "sail around" in the sense of 'sail within' suggests exploration, and the sea is usually quite featureless. "Sail around on the sea" seems more natural to me to suggest moving randomly.

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