Museums
Shandong Provincial Museum
Sometimes has travelling exhibits of interest. Check out the calendar dating from 134BC, and bronzes from the Shang and Zhou eras 1766-770BC. That is old.
Scientific and Technical Museum
Or just browse the interminable shiny floored shopping malls, such as the Silver Plaza next to the Hotel Sofitel, near the Square, and marvel at the new wealth of this emerging powerful nation.
Other
Daming Lake Park
Large park with pagodas, temples and an amusement park. The largest Taoist temple in Jinan is located here as well as a temple in memorial of some local official. Also large natural lake formed from a number of springs and with a large fountain. There are boats for rent. Nice landscaping with willow trees and lotus flowers. Festivals and exhibitions take place in the park. Paid 30RMB is only western and northern half of lake, which is much more crowded and more noisy than nice, relaxed and free ! eastern and southern bank of lake, it's tourist scam one would expect less tourists in paid section and not opposite and avoid visiting paid section and enjoy relaxed beautiful eastern and southern part, there are also tons of overpriced street stands in paid section with double/triple prices of icecreams/drinks.
Thousand-Buddha Hill
A small hill with many steps you can climb to view the smog haze and overlook the city itself on clearer days. Allow about half and hour to reach the top. Features temples, caves, pavilions, terraces, towers, and er Buddhas. On the eastern side of mountain stands the Shandong Revolutionary Martyrs Cemetery for Revolution of 1911, a key historical relic site under provincial protection. Other scenic spots on the Mountain include the Tang-Dynasty Pagoda Tree Pavilion, Shandong Nine Clouds, and Cloud Passing Zen Temple, etc. If you prefer a bus ride, then you can go by bus to the top of the mountain along a mountain road winding up the eastern side of the mountain. A ski lift system and a slide also operate on the mountain, so if the buddhas get boring, you can always slide down the mountain.
Spring City Square
A great place to go any weeknight, and observe why China has relatively few obese people. You can join people dancing, playing many sports, writing poetry calligraphy with water, etc. Bring umbrella/cap during daytime since there is missing almost any green in square resembling visitors unfriendly Tiananmen square. In centre of square is underground supermarket and McDonald's and other shops.
Further away
Hongyegu (Red Leaves Valley)
Beautiful area which is always in a splendour of color in the fall. Red Leaf valley is a private park which encompasses mountains and lakes of great beauty, as well as a rare bird sanctuary. However, getting there is next to impossible without being fluent in Mandarin or having a Chinese translator due to the obscure address of the bus service and the weird rule of having to buy your tickets one day in advance. If traveling by car even a fluent Mandarin speaker may have difficulty in understanding directions: the local dialect is impenetrable!
Longdong Cave
Apparently good in Autumn
Jinan Zoo
Horse Running Mountain
Boasts the Jinan Wild Life World forest safari park and is first class even in Asia."
Five Peak Mountain
Peaks, pavilions, terraces, bridges, including the fascinatingly named Fairy-Greeting Bridge.
Four Door Pagoda
Constructed in 611AD Sui Dynasty with Buddha, and 1000 year old pine tree.
Lingyan Temple
Founded about 1600 years ago and "one of the Four Scenic Spots of Temple in the World". Pavilions, bridges, halls, ponds, terraces, Buddhas, stone tablets, caves. The attractions include "One Line of Sky, Double Pine Bridge, and other grotesque spots like Spring on Mirror Pond.
Springs
Baotu Springs
Has several temples and pavilions. Especially beautiful late in the afternoon, when the locals come to hang out with their feet in the river. Avoid at weekends or Chinese holidays, when it is impossibly noisy and crowded.
Jinan has 72 springs and is famous for them from ancient times. However, nowadays some of them do not have much water.
Five Dragon Pool
It has a very deep pool of spring water and a few natural springs. Very tranquil park with lush greens and ancient Chinese architecture. It also has a temple for a Tang Dynasty army general Qin Qiong who was living in Jinan. In summer, people can walk on the stone tiled floor with spring water flowing on them and kids can have water fights. Beautiful and relaxed place even during chinese holidays.
Hero Mountain (Yingxiongshan)
Good for a climb and a stroll. On weekends it's overcrowded so choose a weekday. Also nearby is the Jinan Hero Mountain Culture Square, a shopping area known as the "Culture Market" see below under Markets.