One of my favorite spots for a quick snack and cheap glass of wine is on Via dei Neri, at All'antico Vinaio. This little spot is open on/off during the day, then from 5-8:30ish in the evening.
You can have a 2 euro glass of wine with some delicious snacks like fried gorgonzola balls, tartufo crostini, and artichokes hearts. These only cost around .70 cents each.
You take what you want on a small wooden plate then sit outside to enjoy the people watching. Once you are finished, tell the young man Tommaso behind the counter what you had to eat and he gives you the total! Similar to the honor system the Spanish use during the tapas crawl. Enjoy!
Via dei Neri #65r