While booking a hotel room, request that the property install a portable fridge with a little freezer shelf in your room. If you are unable to get a confirmation from the booking agent that the property does indeed have these fridges, request that they check and call you back.
Do be as specific as possible on the requirements, as many hotels have mini-bar fridges, but that option is usually insufficient, as it won't freeze your milk or keep your milk cool enough, especially if you traveling for a few days. Here's a picture of what an ideal fridge would look like. The freezer shelf and compartment is very small, but wil work perfectly for freezing milk.
Some hotels also have a special concierge fridge that is used exclusively for breast milk and medicine. This is also a great option, as long as you are able to access your milk 24/7. Do ask if this is an option for you.
If the hotel suggests that they store your milk in their kitchen freezer, let them know that it's not a sanitary solution, and that you'd much prefer to have your own in-roon freezer unit.
Some hotels may say that although they have them, it is on a first come, first serve basis. In that case, I let them know that it's for storing my breast milk, and that I absolutely need to be guaranteed one. This has worked for me in guaranteeing the fridge, since it is for a medical purpose. It is a good idea to call the hotel a few days before your actual check in date to remind them of this request.
Check out the B.A.T.Moms supporters page for information on specific hotels that are breast milk friendly.
While at the hotel, if you're not traveling with baby, or won't be using your milk immediately, I recommend freezing your milk in bags designed for breast milk storage. Lay them flat in the freezer compartment to conserve space. I've always used Lansinoh for my bags, because they come in smaller packaged bags of 25, which are easier to carry around.