Orienting yourself in Jinju is easy. The town is cut in half by the Nam River (Namgang), with Jinju Fortress, downtown, most hotels, the commercial-residential sprawl and the intercity bus station all on the north bank. The train station and the express bus station lie on the south bank.
Bus is the easiest way of reaching Jinju. There are departures every ten minutes from Busan's Seobu (Sa-sang) terminal (1.5h, W6900) and from Masan (1h, W4000), as well as every 20-30 min from Seoul's Gangnam Express Bus terminal (4h, W20000). Check which bus terminal you will be arriving at as the Intercity Bus Terminal is centrally located within walking distance of Jinju Fortress while the Express Bus Terminal is located a bit further out.
Jinju is a small city, so if you have a detailed street map, you can simply get around on foot. Buses are available but you'll find it hard to use it unless you speak Korean, since bus stop signs are almost exclusively in Korean and your average bus driver won't speak English. Taxi is a good option as well, it's unlikely that you will pay more than 5 USD.
Most sights in Jinju are located on the grounds of the Jinju Fortress (진주성 Jinjuseong), at the west end of the north bank. Jinju's moment of glory came in 1592 during the Imjin War, when a force of just 3,800 Koreans held off an invading army of 20,000 Japanese. Unfortunately, the Japanese came back the next year with an army of 70,000 — Jinju was finally crushed and all defenders were killed or committed suicide. Admission to the fortress grounds costs W1000, open 9 AM to 10 PM daily. Parking is available in front of the fortress, at 500won per 30 minutes for small and medium sized vehicles, and 1000won per 30 minutes for large vehicles. The night scenery of the Fortress is also a breathtaking sight and a must-see.
A few sights of minor interest are scattered elsewhere around town.
There´s an excellent silk outlet across the street from the fortress(촉석루) towards the main bridge. The prices are good and the quality and selection are excellent. If you want to experience a local traditional flea market, you could swing by "Joong-Ahng-Shee-Jhang (중앙시장)". Also, there are many little shops (가게, 상점) through out the city where you can buy goods.
Jinju has its own version of bibimbap (비빔밥), which is rice topped with all sorts of goodies. The Jinju style, also known as kkotbap (flower rice) or chilbohwaban (seven-color flower rice), is distinguished by using raw meat! (Not to be confused with the rather more famous Jeonju bibimbap.)
Another local delicacy is broiled eel (장어구이 jangeo-gui), eaten bulgogi-style with a dab of gochujang paste and wrapped in a sesame leaf.
Some people say that the tap water is drinkable, but others would recommend drinking bottled water, which is widely available.
If you are adventurous and need a really cheap place to stay, try one of the jjimjilbang (co-ed sauna rooms) around the city. Jjimjilbang typically cost W8000 and up, for which you get a pair of pajamas to wear, full use of the sauna, a locker to put your possessions in, and a floor to sleep on. One such jimjilbang is Theme Spa Land (테마건강란드), which has a good sauna.
There are lots of gaudy love hotels/yeogwan along the riverfront on both sides of the bus terminal. Rooms from W25,000 and up. Among these, The Versace Motel (베르싸체 모텔) is recognisable for it's romanesque frontage, complete with pillars and small balconies. Located right next to Jinju Bridge in the city centre, rooms start at around W40,000, but are large, clean and offer the best views of the river - especially during the festivals.