Well, it depends a bit on what you like to do.
If you like a theme park athmosphere, then the already mentioned Window of the World is nice enough (lots of miniature buildings, a terrifyingly rickety 1/3rd scale Eiffel tower and a dance show in the evening), as is "Splendid China" which is a similar thing intended to introduce different ethnic groups in China.
There is also a quite impressive light & water show (with dancing) at OCT Bay (but it's a bit aimed at kids).
OCT Bay is a nice area for eating in some nice restaurants (the Korean restaurant there is a good one) and just general evening strolling. There's an Ole supermarket there which is fun to browse through as they import food / snacks from around the world. There's a big Imax cinema there too but you probably wouldn't want to waste your time watching movies
OCT Loft is a very pleasant "artsy" area with different cafes, restaurants and galleries.
MixC is a giant mall, fun for some window shopping.
The botanic gardens are nice (but huge, lots of walking).
Public transport in Shenzhen is excellent so I would recommend staying somewhere along the green line between "Window of the World" and "Laojie" stations, that way you will have easy access to the major sites.
If you feel like splurging, the St. Regis hotel is on the top floors of the previously tallest building in Shenzhen so you'd get amazing views. If you just want to check out the view you can visit the bar at the top, you have to buy a fairly expensive drinks/food voucher in the foyer to get access but it's worth it for the view. I've also heard good things about the Westin hotel located at Window of the World station.
In terms of food, if you like beef, I recommend trying the Chaoshan style hotpot (Chaoshan is a few hours up the coast from Shenzhen, so it's still sort of local). It's based on a beef stock base rather than the typical Chinese "pot of chili oil" hotpot which will make you feel very ill the next day. And if you see anyone selling "pineapple on a stick" then go for it, they're local pineapples and really tasty. Dragonfruit is also local to Guangdong province.
Let me know if you fancy an "eevblog mini-meet" while you're here, we could grab a beer or something