The Surface 2 has a micro HDMI output, however some cables will not work correctly due to the angle of the port.
I picked up a Surface 2 the other day. Loving the tablet, except had few annoying issues. The first was that when I connected it to my TV via a micro HDMI to HDMI cable I picked up on Amazon here I found that it did not work properly. An LG TV worked fine, but a Samsung did not detect the input. It turns out that this is because of the angle of the port, and the fact that the cable needs to be fully pushed home to work properly. Once I worked that out, it was a simple fix with a knife to trim some of the cable shrouding off on one side, allowing the cable to push further in.
Here is the cable after the mod, with one side shaved off, now works perfectly:
The second issue I had, was that my display settings kept getting messed up, either changing the resolution, or making the desktop and start screen much smaller than it should be. This was because I had a Windows 8.1 VM logged on with my account, and it kept syncing the settings. Modifying the sync settings to not sync display settings resolved this one.