Opatija. With a population of around 10,000 people and about 9 miles (14km) west of Rijeka, Opatija was once upon a time the grand dame of Croatian tourism. It was the most fashionable seaside resort during the Austro-Hungarian Empire and many fine hotels, residences, and houses were built there during that period. European royalty also stayed there then, as did celebrities (well, back in the day!) such as the singer Gigli, the dancer Isadora Duncan, and composers Mahler, Puccini, and Lehar.
The place has retained much of its glamour, which means that some hotels can be a little pricey. If you’re on a budget, private accommodation is a more suitable choice – info can be obtained from the tourist office in the center of town.