The Titanic Quarter is where Belfast decided to stop apologising for its industrial past and turn it into something worth visiting. The centrepiece is Titanic Belfast, the museum built in the shape of the ship's prow, it's genuinely impressive from the outside, and the interior exhibition is thorough enough to take a few hours. But the slipways where the ship was actually built, the dry dock, and the SS Nomadic (the last surviving White Star vessel) are all part of the quarter too, and they're worth your time independently.
The waterfront walk stretches along the River Lagan and the docks and gives you a perspective on the city that the centre doesn't. The architecture of the Titanic museum catches the light differently at different times of day, golden hour here really does deliver.
You can walk most of the quarter for free. The museum entry costs, the SS Nomadic costs; the walk, the slipways, the architecture, free. Come on a dry day, bring a camera, and spend a morning.