There's been a hotel of sorts on this prime site since Roman times, and the Duchi remains Trieste's grand dame. Public spaces are hushed and intimate, and the rooms are opulently traditional – the way repeat visitors like them. The bathrooms might be a tad frumpy for some five-star tastes, but the moody basement pool is a good trade-off.
Next door, the Duchi has a modern offshoot, Hotel Vis a Vis, with small-ish but luxurious, all-mod-con rooms. A great choice if your tastes tend towards the contemporary, but you'd like in on the Duchi facilities.
