At the epicenter of downtown’s swiftly gentrifying Old Bank District is Pete’s Café and Bar, a drinking and dining establishment that has ushered in the neighborhood’s future by paying homage to its past. Pete’s spacious dining room would make any history buff smile with original mosaic floors, dark-wood paneling and black-and-white photographs of downtown at the turn-of-the-century. But the mirror-backed wooden bar serves up all of the latest concoctions. Pete’s is down for the long haul pumping out gourmet comfort food morning, noon and night until 2 a.m. On Tuesday night, the whole scene gets jazzy with sets by live bands.