aliko,
What to do in Shenzhen? There's some great places to eat, ask for 'Hua Fa Lu' in town as there are many varieties of Chinese restaurants there, a very good Hunan one if you like it spicy

Nearby is an area called SEG, lots of phones and electronics but costs more than HK.... In the same area is the imaginatively named 'Mans World', 'Womans World' and 'Childrens World' All sizeable shopping complexes with loads of shops specialising in clothes. Some excellent quality and cheap products.
Also there is an area called 'Dongman' fairly near the border, lots of shops for shoes, clothes etc. and some food and electronics places. Watch your bags though as it's famous for pickpockets !
If you have someone with you who speaks Putonghua then taxis are best for getting about, if not you could maybe arrange a guide for the day through one of the bigger hotels like the Shangri-La. Give them a call.
Andy