Which wallet application lets you send to multiple output addresses with just 1 fee? Which wallet applications lets you send to multiple addresses from one output? I'm looking to build a physical bitcoin kiosk faucet and was looking to see how I would avoid miner fees if i combined all the faucet output addresses into just 1 transaction.

I'm sure you can do it with bitcoin core, but was wondering if other wallet apps like blockchain.info and others can do the same?

And what would the command be to send a transaction with multiple output addresses for bitcoin core?
You asked two questions, I can answer only your second question: the command for sending to multiple addresses using bitcoin core.

It is done by building a "raw transaction". This sounds and looks much more difficult than it is in practice. It involves the following steps:


Select enough unspent outputs to fund your transaction
Select the addresses and amounts you will be sending
Add an extra txout with your address and change minus the fee (to prevent sending all change to the miner) 
Build a raw transaction using the unspent outputs and list of addresses and amounts
Sign the raw transaction
Send the raw transaction into the bitcoin network


You will have to do some programming for step 1,2,3.
Bitcoind will handle step 4,5,6.

You can follow the steps in this excellent demo: https://people.xiph.org/~greg/signdemo.txt

Good luck!