You can find many traditional markets in Semarang. The largest one is Pasar Johar. You can find local delicacy in every local market. If you are adventure enought, try tiwul, sego jagung, tempe gembus, urap, etc. I also suggest you to try Soto Semarang which easy to find since they are everywhere, Lumpia gang Lombok, Nasi Ayam jalan Mataram or jalan Melati, Bandeng Presto on jalan Pandanaran, tahu pong on jalan Gajah Mada. But I remind you that Semarang delicacy mostly taste sweet because we love to use sweet soy sauce alot.
As for shopping, there are some good locations but do not compare it with mall in Jakarta or Surabaya. Paragon on Jalan Pemuda, Citraland and Simpanglima Mall in Simpanglima and DP Mall on Jalan Pemuda. E Plaza in Simpanglima is pretty decent entertainmen place. However night life in Semarang is quite dull.
You can also visit Lawang Sewu in Tugu Muda, toko Oen on jalan Pemuda, Railway museum in Ambarawa, Coffe plantation Banaran in Bawen.
Hope you can have wonderful stay in Semarang.