I am not sure if you are going to find a DAC you can plug an iPad or iPhone directly into. You can add an Apple TV or a Bluetooth adapter to any DAC that has a Toslink input.

I personally like the Peachtree DAC iTx and they have a BT-1 Bluetooth adapter. New, the total would be $399.
Creek makes some nice headphone amps and you could get the OBH-11 for $250. I am a big fan of the Peachtree DAC for the money and I am offering a secondhand recco on the Creek from a separate thread I posted. I am still sorting through exactly what equipment I am going to use to round out my system but I am likely to get an OBH-11.

There are standalone units at lower and higher price points that are DACs and Headphone Amps. Again, if it has a Toslink input, just add an Apple TV.

Hello Luke, what kind of price range are you looking at for the headphone amp / DAC? Because the Oppo HA-1 headphone amp/DAC is an awesome unit especially for the price. It has a front USB port that's compatible for iPhone, iPad & iPod. There's another USB input on the back which is asynchronous usb dac. It retails for $1200. Well built. Great sounding for the price. Oppo is very well known for making affordable great sounding components. This Oppo HA-1 implements fully balanced design circuitry. The internal analog audio signal path is fully balanced. For digital audio, the signal runs in balanced mode all the way from the DAC to the output jacks. It has good DAC implementation, design and configuration. The unit uses discrete class A amplifier. The heart of this unit is a custom made toroidal transformer power supplies. It mates well with the Oppo PM1 headphones which retails for $1100. I did listen to this combo before at the local hifi shop and they sounded great together. But you can use other high performance headphones too with this unit. It has plenty of clean power to drive even the most demanding headphones. Highly recommended. You can bypass the headphone amp section and use it as a standalone stereo DAC for your hifi system. There are other high performance headphone amp / DAC units out there that will outperform this Oppo HA-1 but they usually cost much more. Give them a listen for yourself.