I am seeking a device which will allow me to connect an ATMega-based system (very similar to Arduino) to a tablet by hosting it's own network. I like how the GoPro cameras work such that you connect to it and put in the password and you can then change settings on the camera.
I've looked at the products on SparkFun, which include the WiFly, Xbee, and CC3000 breakout boards, but I'm not sure how to determine whether the hosting functionality is possible.
Speed is definitely a factor in this application, as it must be able to feed the most recent information from the Arduino board quickly.
Well, that depends on how much/what kind of data you want to transfer. But generally speaking, I think the limiting factor of the question, whether hosting is possible or not is the capability of your Processor, as the processor will be required to do the hard work, preferrably without influencing the original application.
For the actual transmission of the data, you have several possibilities. I would start with evaluating WiFi and Bluetooth, which both have their advantages and drawbacks, depending on the requirements. A Simple comparision Table you'll find e.g. here Bluetooth vs Wi-Fi - Difference and Comparison | Diffen
Bear in Mind, that with Bluetooth you'll need to write an App for the Tablet, while with WiFi you could go for a local Web Server that does not require a dedicated app.