You'll find millions of bandana on ebay. I always wear one under my helmet in the summer (with sunblock on my ears) – or I'll use a basic welders cap like this.
Not quite the cachet of a cycling cap, and obviously you cant' wear it the other way around, to have the peak as a kinda havelock to protect your neck from the sun on huge, endless climbs like you can with a cycling cap, but they are lighter weight (and flash-retardant if you like ending the ride with a fire).
A buff'll be too much at this time of year – ideal late autumn / early spring tho' as you can tug it down over your ears for the descents.