With a silver tin ceiling and a wood floor seasoned with beer, Grassroots Tavern's basement surroundings have been the East Village's living room since 1975.  Friends get together over tables carved with three decades of hieroglyphs, or challenge each other at one of the three dart boards.  The clientele might include regulars dating back to the '70's, academics from nearby universities, grizzled painters who remember this as a gathering place for major artists in New York City's art heyday.  Or they might just be tourists, bankers, or 20-somethings dropping in after work.  Not a place for snobs or the fashion-conscious, Grassroots stays mellow with one of the best juke boxes in the city, and offers up a menu of some of the least expensive topflight beverages in the region. [map]