Whenever I visit a new area, I like to get the "bird's eye view". The Bunker Hill Monument is a "historical" way to get a good city view. The nearby Blue Hills Reservation provides great hiking, plus the highest point in the area for a panorama of Boston. Walking along the Charles River (Boston or Cambridge side) is always nice, especially in good weather. Unfortunately, the Hancock Tower (with the highest building in Boston) shut down their viewing platform soon after 9/11.
Blue Hills Reservation provides great hiking and vistas of Boston. At 635 feet above sea level it may not sound high by Western US standards, but it's actually the highest point along the Atlantic coast south of Maine. Going to the top from the Trailside Museum or Park Headquarters is a very reasonable day hike, and can be done with children (I've gone with 4 year olds - just take it slow).
Bunker Hill Monument is in Charlestown, at the end of the "Freedom Trail". Make sure you have enough energy left to climb to the top for the view!
The Esplanade is one of my favorite places to walk, hang out, and play ultimate. All season round excellent. Across the river, walk along Memorial Drive in Cambridge, and stop at the Royal Sonesta Hotel for a gander.
The Hancock Tower observatory closed after 9/11, but it's still worth a visit (it's right in Copley Square) to see the I.M. Pei architecture.
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Blue Hills. By Car (easiest):
Rt. 128 to Exit 3, Houghton's Pond. Turn right at stop sign onto Hillside Street. Houghton's Pond is approximately one mile on the right. Or continue to reservation headquarters on the left next to the MDC stables. By MBTA/Bus: West area-Red Line to Ashmont Station, high speed line to Mattapan, take Canton and Blue Hills bus to Trailside Museum. For Houghton's Pond area, stay on the bus and exit at Hillside Street at Howard Johnson's. Cross at light and walk one mile east on Hillside.
Bunker Hill Monument. Orange Line to Bunker Hill, or walk the freedom trail.
The Esplanade. Head for the Charles River until you get there - from Beacon Hill, Back Bay, or whatever.
Cambridge Side. Cross over at the Museum of Science, or on the Mass. Ave. bridge (nice view, a bit busy).
Great day hike - pack a lunch. Start, if you can, at the Trailside Museum, and ascend to the Eliot Observation Tower. It was constructed in the 1930s by the CCC (Civilian Conservation Corps) of local stone, and provides really spectacular views of Boston.
About 1/2 mile further up the trail is the Blue Hill Weather Observatory (http://www.bluehill.org). Originally built in 1885, it's the oldest American weather observatory in continuous use. There are now more formal tours of the library and roof deck during daylight hours, Saturdays and Sundays (Adults: $3, Children 5-17: $1.50, Under 5: free). If you go on a windy or rainy day you can usually get to it yourself. On the roof, my favorite is the 'pyroheliometer', a glass orb through with the sun burns a strip of paper to estimate of the number of hours of sunshine each day. If you do wish to visit during the week (Monday through Friday) you must call first to make an appointment at 1-617-696-0389.
The Trailside Museum (run by the Massachusetts Audubon Society) has interesting exhibits, including live animals such as Snowy Owls. There are also special programs throughout the day. Check the Mass Audobon website at http://www.massaudubon.org for the latest program information - search for "Choose a Sanctuary", then "Blue Hills". The cost for entrance to the museum is $3 for nonmember adults, $2 for nonmember seniors, and $1.50 for nonmember children. The Nature Center is open Wednesday through Sunday, 10 a.m. to 5 p.m.
It sounds strange, climbing a 221-foot granite obelisk... But it's actually fun, and there's even a bit of history in it, as it marks the site of the first major battle of the American Revolution. You're rewarded at the top with some narrow windows and views of the new "Big Dig" Leonard P. Zakim Bunker Hill Bridge.
The visitor lodge and exhibits are open daily, 9:00 a.m. - 5:00 p.m., except on Thanksgiving, Christmas and New Year's Day.
The monument is open to climb from 9:00 a.m. to 4:30 p.m. daily. Best of all, admission is Free.