The red line of the Boston subway (or the T as it is called locally) serves Cambridge. Stops between Kendall/MIT and Alewife are in Cambridge. 
The Fitchburg line of the MBTA commuter rail has a stop in Porter Square. This line serves the northwest suburbs and ends in Boston's North Station where you can connect to other northbound commuter rail lines. 
MIT Museum 265 Mass Ave. (Central Sq), 617-253-4444. Has a huge collection of holography, a hall of hacks (practical physical jokes that get placed around the institute -- like the police car that once graced the top of the great dome is in the hall of hacks), plus rotating exhibits. http://web.mit.edu/museum/
Harvard Museum of Natural History 26 Oxford Street, 617-495-3045. Contains the Botanical Museum (home of the famous glass flowers collection), the Mineralogical & Geological Museum, and the Museum of Comparative Zoology. http://www.hmnh.harvard.edu/
Busch-Reisinger Museum 32 Quincy Street, 617-495-9400. Devoted to promoting the informed enjoyment and critical understanding of the arts of Central and Northern Europe, with a special emphasis on the German-speaking countries. http://www.artmuseums.harvard.edu/busch/
The Fogg Art Museum 32 Quincy Street, 617-384-8310. Western art from the Middle Ages to the present, with particular strengths in Italian early Renaissance, British pre-Raphaelite, and nineteenth-century French art. http://www.artmuseums.harvard.edu/fogg/
Washington Elm Cambridge Common at Mason St. On July 3, 1775, Washington officially took command of the Continental Army at ceremonies beneath the tree, which stood at the edge of the training grounds used by the troops. A small bronze plaque marks the spot. The history of the Washington Elm is included in the "Harvard Book," the electronic history of Harvard and its surroundings.
Longfellow National Historic Site National Park Service 105 Brattle St. 617-876-4491. Washington made his headquarters here during the siege of Boston from July 1775 through April 1776. From 1837 until 1882, it was the home of poet while he taught at Harvard. The site's collections deal mainly with Longfellow, but there are some Washington letters as well.
The Boston Phoenix Free weekly and web site (http://bostonphoenix.com/) listing concerts, theater plays, movies, restaurants, etc.
With a dizzying array of options, and slightly less stringent liquor laws, Cambridge is every bit as much a dining destination as Boston. Most restaurants tend to cluster around Harvard and Central Squares, but if you're willing to stray a bit beyond the subway stops (and you should be), you'll quickly discover many less-travelled neighborhood gems. There are a number of Indian restaurants along Mass Ave. between Central and Harvard Squares, of varying quality.
Anna's Taqueria. 822 Somerville Ave. (Porter Sq), 617-661-8500. Fast Mexican food, much better than Taco Bell. People seem divided on Annas, some love it, some hate it.
Beauty's Pizza, 228 Broadway. (Kendall Sq), 617-876-6969. Mo-Th 11AM-10PM, Fr-Sa 11AM-12AM, Su 5PM-10PM. Delicious pizza, oven-baked subs, and fresh salads. Take-out and delivery. See the full website and menu at beautys-pizza.com.
Mary Chung's. 464 Mass Ave. (Central Sq), 617-864-1991. Closed Tuesdays. Super-yummy Chinese food, including Dim Sum on 11:30am-3pm on Saturdays and Sundays. A full menu is available. Signature dishes are Dun Dun Noodles and Suan La Chow Show. A major hangout for MIT geeks, and thus the first restaurant with a Usenet newsgroup, alt.fan.mary-chungs. Don't forget the pot stickers. Cash only.
Cinderella's, 901 Main St. (Central Sq), 617-576-0280. Su-W 11AM-1AM, Th-Sa 11AM-2AM. Pizza, subs, and good "American" Italian cooking. Pizza slices aren't on the published menu, but are available for a scant $1.25 and only $.25/topping. Entrees $5-$10. Open late.
Moody's Falafel Palace, 25 Central Sq, 617-864-0827. 11AM-12AM daily. Located in a tiny "castle", this inexpensive Middle-Eastern restaurant serves up delicious shawarma, kebab, and their namesake falafel. Sandwiches $3-$5, platters $5-$7.
The Middle East, 472/480 Mass Ave. (Central Sq), 617-864-EAST. Su-W 11AM-12AM, Th-Sa 11AM-1AM. This legendary Cambridge institution consists of an art gallery, 3 live music venues, 4 full bars, and no less than 3 dining areas (including the upscale Zuzu, below). Sample a large variety of Lebanese dishes served in a vibrant, artsy setting. The "Corner" dining area (enter at 480) features live music every night, often free, with belly dancing on Su and W. Extensive vegetarian menu. $4-$12. (See also the Drink section). http://www.mideastclub.com/
Grendel's Den, 89 Winthrop St. (Harvard Sq), 617-491-1160. M-Sa 12PM-1AM, Sun 4PM-1AM. Serving basic American bar food, this dark and crowded Harvard tavern would be unremarkable if it weren't for their incredible happy hour special. From 5PM-7:30PM everything on the menu is a paltry $3 with a beverage purchase of $3 or more. If you can get a table, that is. Non-happy hour entrees $5-$8.
Picante Mexican Grill. 735 Mass Ave. (Central Sq), 617-576-6394. Good and healthy Mexican food, a step above fast food.
Veggie Planet, 47 Palmer St. (Harvard Sq, Inside Club Passim at Church & Palmer Streets), 617-661-1513. 11:30AM-10:30PM daily, brunch Su 11AM-3PM. Didi Emmons, author of Vegetarian Planet, is the owner and head chef. Completely vegetarian and mostly organic, with plenty of vegan options (they'll substitute tofu "ricotta" for other cheeses). Yummy veggie combinations served over whole-wheat pizza dough, brown, or coconut rice. Lunch runs about $6, dinner $10. http://www.veggieplanet.net/
The Porter Exchange, 1815 Mass Ave. (Porter Sq). M-Sa 12PM-9PM, Su 12PM-8PM. The food court of this indoor shopping area is the closest thing to Tokyo in Boston. A half dozen stalls compete to serve up delicious and cheap portions of tempura, udon, sushi, ramen and bulgogi without any frills. Finish your unagi-don (eel over rice) with a scoop of ginger mochi ice cream. $3-$7
Atasca, 2 locations. 50 Hampshire St. (Kendall Sq), 617-621-6991. M-Sa 11:30AM-11PM, Su 12PM-10PM & 279A Broadway (b/w Central & Inman Sq), 617-354-4355. Tu-Sa 5PM-11PM, Su 5PM-10PM.
Emma's, 40 Hampshire St. (Kendall Sq), 617-864-8534. Tu-F 11:30AM-10PM, Sa 4PM-10PM. This cozy little pizzeria stands out for two reasons: Unique and sometimes bizarre topping combinations (like the house-smoked bacon pizza with roasted gold potatoes, cilantro and dried cranberries) will make you rethink what makes a pie. And, more importantly, the pizza here is actually good -- the crust is thin and crispy, the sauce is flavorful, and the cheeses are fresh and melt just right -- quite a feat considering what typically passes for pizza in the Boston area. $8-15/$11-18 (small/large pie).
Mr. Bartley's Burger Cottage, 1246 Massachusetts Avenue (Harvard Sq), 617-354-6559. M-Sa 11AM-9PM. A Harvard Square landmark, Bartley's serves practically any kind of hamburger you can imagine, most named after individuals. A favorite - The Ted Kennedy - "a plump, liberal amount of burger with cheddar cheese, mushrooms, cole slaw and french fries." $10-15. http://www.mrbartleys.com/main.html
Border India, 781 Main St. (Central Sq.), 617-354-0405. 11:30AM-10:30PM daily. Indian food, highly recommended. An online menu is available.
Zuzu, 474 Mass Ave. (Central Sq), 617-864-3278 x237. 5:30PM-11PM nightly.
Bambara, 25 Edwin H. Land Blvd. (In the Hotel Marlowe near the Cambridgeside Galleria), 617-868-4444. Su-Th 5:30PM-10PM, F-Sa 5:30PM-11PM.
Harvest, 44 Brattle St. (Harvard Sq), 617-868-2255. M-Th 12PM-2:30PM, 5:30PM-10PM; F-Sa 12PM-2:30PM, 5:30PM-11PM; Su 11:30-2:30, 5:30PM-10PM. Regional contemporary American cuisine, with an emphasis on fresh, seasonal ingredients. A wonderful outside dining terrace and one of the best Sunday brunches (prix fixe, $33) in Greater Boston. Lunch $20-$30, dinner $40-$60. http://www.the-harvest.com/
Oleana, 134 Hampshire St. (Inman Sq), 617-661-0505. Su-Th 5:30PM-10PM, F-Sa 5:30PM-11PM. Oleana's inspired and exquisite offerings span the Mediterranean from Spain to Turkey and Armenia to North Africa, yet everything comes together superbly. Vegetarian prix fixe ($38) includes 5 mezze and dessert. Omnivorous entrees $21-$25. http://www.oleanarestaurant.com/