Welcome to Boston! Depending on where you live, but there are a few decently sized Starbucks around town. My fav in town is actually the big one on Boylston St, not only because it's big but their wifi doesn't suck. Just stay away from the big one in Harvard Sq as their wifi is almost always overwhelmed.
I know SB's aren't to everyone's taste. I like to work out of the Boston Common Coffee locations, both around Downtown Crossing. They have really good food.
Also, you're likely to gravitate towards Kendall Sq in Cambridge since it's the epicenter of startups in Boston. There'a couple of good coffee shops there with excellent coffee. Both are on the same street, 3rd st. One's called Voltage and the other is Tatte. Tatte is a little smaller but stil has wifi and terrific food. There's also an SB in Kendall square that has a decent amount of tables and wifi.
If you're after paid space, there's Workbar across the road from South Station. I think they charge around $20 per day for a desk. I've been there for a few events.
Finally, if you're not needing to be on the phone all the time, try the Boston Central Library in Copley Sq, it has good wifi and obviously lots of quiet working space.