Mountain bikes give you nice fat plush tires and tend to be priced well. Ditto goes for quality hybrids; the price tends to be right and you can get a pretty fat 700c tire to work on most of them.
Vintage road bikes (think 70s era which often come with center pull brakes) give you that retro cool look and can take a pretty fat tire (you likely top out at 35c). 650b conversions are also a possiblity.
Or you can find one of a very rare breed, a vintage bike designed for gravel and mixed surfaces. The Bianchi project bikes and Bridgestone XO series provide two examples.