Slovenia is not a big country but you need a car to visit it, unless you
want to get to major cities by train and then use the local bus network.
You could also consider to cross the border at Gorizia/Nova Gorica (you can
do it even on foot) and rent a car in Slovenia.
The big garage in the railway station square is reasonably safe and fairly
priced (9$ every 24 hours).
Hotels: My favorite is Hotel Riviera (phone 040-224551), overlooking the gulf, Miramare Castle and with a wonderful private beach in summer. They have private parking and restaurant. Hotel Impero (phone 040-364242)(visited by Don and Linda) is less fancy and has no view, but it's right across the train station, very close to town centre. Parking available at the garage I mentioned before and I think they have a little restaurant. It should be priced about the same as above. There's plenty of other hotels around there, but the area is a little sad and deserted at night, as it usually happens around any rail station in Europe...
Five star hotels: Savoia Excelsior (040-77941) a few meters from main square, facing the sea but has street parking only. Price is high, over 180$ per night. A new one is Greif Maria Theresia, located on the road from Trieste to Miramare in a refurbished 19th century building. The sea is across the road. Has expensive restaurant, health club, private parking etc. The price will be around 200$
Places to eat: Trieste has many buffet, quick service reataurants with a few tables serving hot and cold traditional dishes for working people at lunch. A few are open for dinner, but in this case the prices are higher of course. The seafood restaurants you find on the road coming into town or by the sea downtown are expensive. More details are of course available if you need them.
If you want to try it, a good link is http://www.triestetourism.it . This is the site of Tourist Council; they're friendly and eager to help.