I like my coffee with milk also and first thing in the morning. Calcium is a binder and so probably does compromise your levothyroxine. What I do is take my levothyroxine in the middle of the night when I get up to go to the bathroom. I just lay it out before going to bed with a half-glass of water so I can take with almost without having to fully wake up.
Instructions say to wait 30-60 minutes before having anything other than water. I take my med, then get my shower, etc - by that time 30 minutes has passed and I have my coffee. I know there are some who have coffee right away. I don't know that it really makes that much difference, so long as you are consistent; meaning you do the same thing every day. Probably, the worst that would happen is that your med would not be fully absorbed, which could cause you to need an increase.