Your biggest problem will be getting away from crowds. A whale watch is a good idea. Besides whales, dolphins and seals, you should see plenty of gulls and cormorants with a chance at things like eiders and scoters.
Most of the harbor islands constitute a park, but there is limited boat shuttle service. You'll probably get a better view of the islands on a whale watch.
Don't count on seeing any herons or egrets in Boston Garden. If you get there *really* early in the morning you might get really lucky, but it's just too crowded most of the time. Mallards, geese, swans. (Also city birds like sparrows, starlings, pigeons, etc., and passing songbirds - maybe an oriole if you're lucky.)
There are several other ponds and marshes quite close to the city where you might find a heron, but public transit is a bit of a pain if you've only got half a day. (Much better than most US cities, but that's not saying much. You'll need this:
http://www.mbta.com/schedules_and_maps/system_map/ )
There are a couple of spots on both the harbor and the Charles River where you can rent a kayak, though most of the best habitat is not within easy reach.
edit to add: a number of parks landscaped by Olmsted are popular with birders. This includes not only the Common and the Garden and the Arnold Arboretum (on the Orange Line, Forest Hills stop) but also Mt Auburn Cemetery (near Harvard Square, on the Red Line) [Note the Orange Line is a bit... scruffy.]
further added: If you've got two hours devoted to experiencing downtown, do it on a tour with Boston by Foot. If you've got the least interest in history or architecture, these tours are absolutely top-notch. Some are kid-friendly.