There is a ton of good information in the responses.

I have a Pally team as well and love them. They are still undergeared but my prot is coming along. Your HP seems a bit low.

The dungeons I found I could get badges on were the following. Clearing some of them.

UK
Nexus
Gundrak
One in Dalaran..name escapes me
UP

I just tried to kill as many bosses as I could to get emblems then would upgrade a piece here and there.