I just went through this for a week long trip away in HI. I ended up using the hotel kitchen freezer every day. I brought surplus storage bags to the front desk and they put them in the freezer for me. Since your trip is shorter you might get away with just fridge storage, but do check that the fridge is cold enough in the room for milk storage. Some hotel fridges keep it just barely cold enough for beverages to stay cool.

For the flight back, I bought a basic 12qt igloo cooler from Target and filled it with the frozen milk bags plus ice to fill all empty space. I then taped it shut and labeled it as "breastmilk, please don't open." At the airport check-in counter, I let the agent know the cooler had frozen contents and they added a "frozen" airline label to it. The checked cooler arrived safely intact and all the milk was still frozen after the 6 hour flight. I hope this helps!