When Myrcella was sent to Dorne, she took a ship and the royal family went to docks to see her off. Similarly, when Jaime came back from Dorne, he came in a ship and took a boat to come to the docks.
When Doran Martell was supposed to arrive at Kings Landing, Tyrion was waiting for him and his entourage on a road outside city walls. From the maps, the sea seems to be best way to travel between Dorne and Kings Landing.
Why did Oberyn (who came instead of Doran) choose road travel instead of sea?
Too many banners, he thought sourly, as he watched the ashes kick up under the hooves of the approaching horses, as they had beneath the hooves of the Tyrell van as it smashed Stannis in the flank. Martell’s brought half the lords of Dorne, by the look of it. He tried to think of some good that might come of that, and failed.
“How many banners do you count?” he asked Bronn.
The sellsword knight shaded his eyes. “Eight . . . no, nine.”
He definitely came on land, otherwise he couldn't have taken all those horses--or, for that matter, all those people. It's possible that there are just too many people to fit on a good-sized ship. Or maybe it would just take too long for all of them to get to the coast (from Storm of Swords:)
There were three sorts of Dornishmen, the first King Daeron had observed. There were the salty Dornishmen who lived along the coasts, the sandy Dornishmen of the deserts and long river valleys, and the stony Dornishmen who made their fastnesses in the passes and heights of the Red Mountains.
But the biggest reason is that taking a ship to Dorne isn't normal. Myrcella did it by sailing to Braavos, where she would then take another ship to Dorne. This was probably not common; she did it to avoid Stannis, but Tyrion thinks as she leaves (From Clash of Kings:)
Traveling from King's Landing to Dorne by way of Braavos was scarcely the most direct of routes, but it was the safest . . . or so he hoped.
Even without that, travelling by sea is hard. You need a ship, a crew for the ship, another ship and crew (if you have a princess you need two ships) as well as the rest of the princess's entourage. And there are pirates, storms, and other hazards along the way. In addition, to get to Dorne you have to sail out of King's Landing all the way to the Narrow Sea. Then you have to sail down the length of the Narrow Sea, which is a horrible place with a lot of storms and such. Then you finally reach Dorne, and you still have to pay a bunch of gold to the crews and captains of the ships.
Coming by lad is easier and faster. Just get your entourage and some horses and go south. Eventually, you'll get to Dorne. Yes, there are bandits, but that's why you bring your arrow-fodder with you.
He was sending Ser Arys Oakheart as her sworn shield, and had engaged the Braavosi to bring her the rest of the way to Sunspear. Even Lord Stannis would hesitate to wake the anger of the greatest and most powerful of the Free Cities.