I make and sell Tapster, a delta-style robot that is programmable, 3d printable, and open source. I designed it for testing apps on iOS and Android. If you have more time than money, you can download the plans and make one yourself. Otherwise, I can make it for you. https://www.tindie.com/products/hugs/tapster/
I know that NAO is programmable [1] but I haven't seen where you can buy one. Maybe out of stock.
Even if you could buy one, one of them costs 12k euros last I checked (a few years ago)
Lego Mindstorms is a really popular kit among robot enthusiasts. It's a good starter kit.
There are multiple options available. Mostly depends on what you would be interested in doing. Shoot me an email (address in profile) if you'd like some help figuring it out (I'm in robotics).
I like the uArm, an Arduino powered arm for $340. http://evol.net/
Intel Jimmy/HR-OS1 for $1600 with Intel Edison and Raspberry Pi 2, runs on Linux, has an SDK/AppStore, customizable 3D printed body and planned support for computer vision. Ordered one, next month should arrive, can't wait 8-)