As of May 2010, there are overnight buses from Almaty's Sayran bus station that leave at roughly half hour intervals from 18:00-21:00 everyday. The journey takes approximately 12 hours, KZT2400 [update Aug 2012].
Overnight buses will arrive at the Samal bus station, 5km out from the city center. From there, you can take buses from 35tenge to 40tenge for a marshrutka to the center. Taxis to the center are also available for 300-400tenge.
You can take "gypsy cabs" for 300-400 tenge anywhere in the city. Bargain if they try to overcharge.
Busses run to and from the center and all of the microdistricts. The cost is 50 tenge as of 2013
"Marshrutkas" are mini-busses that run largely the same routes as the busses. They cost 50 tenge as of 2013. They can be very crowded during rush hour (e.g. standing room only, with low ceiling)
Abai Park: memorials, tanks, ferris wheel, statue of Abai. Attached is the aquapark "Delfin" if you want some water park fun in the summer
Park Ken-Baba: some miniatures of famous architecture, as well as a little pond and walking area with rides/swings. On main road Tauke Xana, and Kazybek-Bi
Mega: most popular youth hangout place in town, a mall with indoor skating rink, movie theater, Western-style chain grocery store and an upstairs food court. On Tauke-Xana
Spartak - awesome outdoor swimming pool, soccer field and basketball court. Across from Mega on Tauke-Xana
The big Tulip Fountain - on the corner of main street Tauke Xana and Mamashuli.
New Memorial - very impressive, at Ordabasy Square, the site of the founding of Shymkent. There is a massive monument recently built that you can get to by climbing up on a bridge past some nice fountains (equally if not more impressive at night). Also see the Philharmonia (though I have never seen a concert here even once), a nice park area, and the new yurt-like museum they built recently, all in that area. Inexpensive shared taxis to Sairam also leave from this square.
Hippodrome -- if anything is going on (which is rare: usually public holidays like Nauryz), the Hippodrome is well worth a visit for horse games such as Kokpar. Hard to find out when things are happening, however.
New hockey/ice skating rink
Old cinema: next door to the skating rink
Markets: Aina Bazaar, good for buying food and random stuff (some clothes, Chinese electronics, burned CDs with Kazakh music, etc.). In a microregion a bit outside of town, but public transport regularly goes there. Koktem bazaar is good for fresh produce and fruit.
"Cinema Bar": a European-esque techno club with no cover charge, attached to the old cinema on Zheltoksan and Baitursynova. Has a cool ambience inside, old-movie decor. May be closed now, not sure.
Hotel Shymkent: a fancy club called Joy attached to it, with cover charge
Karaoke bars: down past Hotel Shymkent on Respublika (extension of main street Tauke Xana), bus stop "Ogonyok"
Bowling and pool tables at Tauke Khana and Kunayeva, upstairs at the "Maharaja" entertainment complex right next to the Spartak sports complex in the middle of town
Hookah bar: recently opened in the 17th microregion, expensive but nice ambience and stage with DJ/live music on certain nights/events
Movies: playing (mostly Western movies dubbed in Russian) on the top floor of Mega Center.
"Babylon": arcade complex also on the top floor of Mega Center, complete with games and laser tag
There are good souvenir shops in Park Ken Ba Ba, on Taukexana street. They sell stuffed camels, magnets, keychains, leather goods, plates and figurines.
Kazakhstan is also famous for good, handmade silver jewelry.
Kok-serai - Uzbek restaurant on Ilyaeva and Momyshuli
Caravan - excellent Uyghur lagman (get the Busso lagman, fried with meat and peppers), inside of park Ken-Baba.
Madlen - western-style sandwiches, pastries, salads and shakes. Two locations: Ilyaeva, or the bigger Madlen next to Shymkent Hotel on Tauke-Xana. Very popular Shymkent hangout with locals
Cafe Molka-Кафемолка- Slightly higher prices but much tastier roasts. Also a small selection of high quality treats, breakfast foods, and pricier light lunches. Free wifi. Understated entrance on south side of Tauke-Xana, opposite the southwest entrance to Ken-Baba park.
Mozzarella - expensive Italian food with free wifi, on Ilyaeva and Dulati
El Doro - excellent and reasonably-priced pizza, on Tauke Xana past/across the street from Park Ken-baba. Try the vegetarian with goat cheese
Dinara cafe/bar - pick up a good shashlik (grilled meat kebab) and mug of Shymkentskoe beer, a "typical Shymkent" meal. Right across the street from Mega Center mall on Tauke Xana
+7-7252 is the area code for Shymkent.
Great day trips:
Turkestan: the most famous Muslim site in Kazakhstan, with a beautiful mausoleum and brand new historical museum. Definitely a must-see if you're in the south for a few days.
Sairam mausoleums: you can take a taxi from Ordabasy Square to Sairam for 200-300 tenge. Stop to see the "SHYMKENT" Hollywood sign on your way!
Sauran ancient city ruins - you can book a private taxi from Shymkent, or take a taxi from Turkestan if you're already there.