If you were my client, I would recommend you Waltham area. Most single family homes area around the price range you mention and it is a nice neighborhood close to Boston and serviced by public transportation.
There is lots of info in the Internet and also you want to check police boards web sites to complement your search. A starting site can be: http://www.everyblock.com/
Please contact me to help you finding your new home in the Boston area.
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As far as location and safety are concerned, I always recommend my clients to first identify a few keys areas that they are most interested in and check them out at various times of the day as well as days of the week (a neighborhood can feel quite different on a Saturday night than on a Wednesday afternoon). After they identify the areas that they are most interested in, I advise them to contact the local Police department to get the specific crime statistics for the area - nothing tells the story more than the actual facts.
Gary Dwyer, Broker / Owner
Serving Greater Boston Home Buyers Since 2005
Buyer Agents of Boston, LLC
you can check crime rates on the web. Check out: http://www.cityofboston.gov/police/stats. Some areas that are close to Harvard are Cambridge, Somerville, you can also check out Arlington, Medford.. Also if you are ready to buy I'd suggest getting a buyers' agent to assist you. This will not cost you anything and you will not only be represented but have someone at your side that can answer questions you may have along the way. If we can be of assistance, let us know at email@example.com. If you want to get properties updates on properties on the market as well as sold ones let us know. Best of luck