Once you have turned off the motorway on your way to Trieste, you will be faced with two possibilities: you can either take the coastal road which hugs the shore but is often very congested, or you can climb the upland plains behind the city and eventually make your way back down towards the sea. The latter option is considerably more convenient, but less panoramic.
Remaining in the Viale Miramare, if you are looking to spend a little less there is always the Ostello della Gioventù . It is a typical youth hostel but it has a location to die for: only twenty metres from the sea and a hundred metres from the charming castle which was once the home of Maximilian and Charlotte of Austria.
If you are here on business and you are intending to visit one of the numerous companies or institutes which have sprung up around the Area di Ricerca (which is the last motorway exit before you reach Slovenia), then you should seek accomodation in the guest quarters of the Padriciano science park, where you will perhaps be the guest of the organisation with which you are dealing. Here, you will be far from the city centre, but close to the drawing board.