I've found 2 different travel mugs that work great for bike-carry.

The first is a Trudeau brand SS mug with a twist top system that seals perfectly, and it's easy to open and you can drink from it from any point around the top unlike "sippy lids" which leak and require you drink from one spot. It fits all my water bottle cages fine, but the Profile Design "Kage" works best for holding non-standard water bottles. I can also throw it inside my bag secure in the knowledge that it won't leak.

The other one is a stainless steel caribeaner mug with a twist off cap that is sealed with an O-ring. you have to remove the lid to drink from it which is not as convenient for on-bike sipping or strolling and sipping, but the trade off is that it clips easily to the strap on my bag, or once again can be kept inside the bag without fear of leakage.