Every year in late July-early August, the Commonwealth Shakespeare Company puts on free performances on Boston Common of various Shakespeare works. Performances are well attended, but there are few space constraints so you should be able to find a decent vantage point. Food Trucks show up and picnicking is a popular activity.
BPL
This is the headquarters of the Boston Public Library (BPL). This branch is defined by its two buildings, the original McKim building from 1895, and the newer Boylston building, opened in 1972. They were built to similar scale and use similar materials, but the ornamentation–or lack thereof–clearly separates them. The Boylston building completed extensive renovations summer of 2016; featuring a new cafe, radio station, and other amenities for the people of Boston. Don't miss the beautifully quiet interior courtyard, a place to spend a solitary moment reflecting in the heart of the city.
Christian Science Plaza
This strikingly beautiful site stretches out over almost 15 of the most expensive acres of land Boston has to offer. Functioning as the center of Christian Science in America, which is a metaphysical belief system professing "sickness is an illusion that can be corrected by prayer alone". The Mother Church (1894) and its enormous extension (1906), are architecturally significant, seeming to flow into one another with fantastic detail. The long reflecting pool is great to stroll around and people watch. You'll also find a giant water fountain to the north end of the pool, a real hit with the kids during sweltering summer days.
The Massachusetts State House was built in 1781 on Beacon Hill, land once owned by John Hancock. The dome of the State House was re-gilded with glittering 23k gold leaf in 1997, and makes for a spectacular view at sunset from the Massachusetts Avenue bridge. Free tours are available weekdays all year long from 10AM to 3:30PM, they last about 45 minutes. The grand staircase and hall of flags are a few of the highlights. Make sure to ask about "The Sacred Cod" to get the whole story.
Brattle Square Church
Admittedly a "deep cut" of Back Bay churches, this building houses a congregation formed all the way back in 1665, during a time when being Baptist was a punishable offense. The current building was opened in 1872 and designed by H. H. Richardson, the very same architect of the more famous Trinity church anchoring Copley square. Another notable element here are the friezes seen ringing the top of the tower. These were carved on site by Frédéric Bartholdi, who would later create the Statue of Liberty in New York.
Third Church
As one of the finest High Victorian Gothic churches in New England, the Old South Church is a stunning aesthetic landmark within the Back Bay. The interior is filled with sumptuous materials, musical instruments, and stained glass. After a misguided makeover in the 1950s, a painstaking restoration took place during the late 1980s. Historical members of the congregation include Samuel Adams, Benjamin Franklin, and William Dawes; Paul Revere's lesser known counterpart. (Although this building would be news to them.) Willard Sears, one of the architects responsible for this structure, also takes credit for the Isabella Stewart Gardner Museum, another European inspired masterwork.
Founded in 1809, this Park Street Church is on the Freedom Trail and known for a number of historical firsts. Among other things, William Lloyd Garrison delivered his first anti-slavery address here, and "My Country Tis of Thee" was first sung on the front steps. Very much still an active pro-life parish, it hosts many classes teaching English as a second language, ministers to the homeless, and assists low income families within the city of Boston. Fun fact: this was the tallest building in America for almost two decades!