You may make one Recovery test per condition per phase.
So, if I’m Angry, Afraid, Exhausted and Injured, and I’m entering town with four checks, I can make a test to recover from Angry, but if I fail, that’s it. No more recovery is possible.
Does this mean that drinking at the Tavern won’t help my Angry, since it’s in the same Town phase, pretty much ruining any chance of recovery outside of a Hotel (or magical healing)?
Yes. It’ a risk you take. Magic, vapors and other concoctions from alchemists and so forth are options, of course.
Mad cackling on the part of the DM is optional.
But to clarify, should succeed, you can proceed to roll for the others, correct (until you fail)?
If you have checks left, yes. Much better than having to spend on Lifestyle.
Ooh. But do you have to rotate the checks around like in the camp phase?
Please note that RECOVERY is a specific term and isn’t the same as alleviating a condition through methods Thor described.