One option, if you want a good city topcoat, is a suiting fabric. 13oz or 16oz. You could get a charcoal herringbone, or the same in navy. MAYBE a hopsack. Sometimes Italians do that when they want to look sharp but not overheat. You do have to be careful, as it should look like a coat and not a suit. I was going to suggest Harrison's Oyster, but there may be something similar in the VBC catalogue, or one of the very English books from Holland & Sherry or even Scabal.
If you want very crisp, and are willing to have it not last forever b/c of shine, a cavalry twill from one of the trousering books will be a pleasant step up from trenchcoat cotton and still be graceful enough to roll up easily while traveling on planes, etc.
If you want a little more casual, Donegal tweeds do breathe well. There are players other than W. Bill, but I don't know who they are at the moment. Be careful with Scabal, Dormeuil, and some others-- in addition to the real stuff, they sell "tweeds" that look to be aimed at the disposable ladies' fashion market.