Most cities answer "who fixes the sidewalk" with one rule that covers the whole city. Boston answers it with two, and which one applies to you depends on a classification you probably have never looked up.
The split is public way versus private way. On one, the city maintains the sidewalk. On the other, you do. Same city, same neighborhood, potentially the same block.
Public way: the city maintains it
On a public way, the City of Boston handles infrastructure maintenance. The concrete, the surface damage, the repairs. If the sidewalk in front of your house is broken, you report it. The resident's own obligation is narrow: clear snow along the property line when it falls.
Private way: the residents maintain it
On a private way, the city's own guidance is direct. Residents are responsible for all maintenance of the streets and sidewalks along the private way. All maintenance is doing real work in that sentence. It is not just the sidewalk slab. It is the street, the paving, the upkeep, and the snow.
We are not going to put a dollar figure on the gap, because Boston does not publish one and neither does anyone else who is being honest. But the shape of it is clear enough: on a public way a broken sidewalk is a service request, and on a private way it is a contractor quote.
The only test that counts is the Street Book
Boston publishes the Street Book, a directory classifying every street, way, and alley in the city as public or private. That is the official record and it is the whole answer.
Do not guess from appearances. The classification is historical and legal. A private way can be a well-paved, established street that looks exactly like the public way it connects to. Condition tells you nothing. Age tells you nothing. Your neighbor's confident opinion tells you nothing. Look it up.
What this means when a repair notice shows up
If the city sends a notice about the sidewalk in front of your property, the status of the street is the first fact to establish, before you get a quote or agree to anything. On a private way, the obligation is yours and the notice tracks the published rule. On a public way, the published rule says maintenance is the city's job, which is a reason to go back to Public Works with the Street Book entry in hand and ask them to reconcile the notice with their own guidance.
That is not legal advice and it is not a promise that the notice goes away. It is just the order of operations: confirm the classification first, argue second.
Why Boston is unusual
None of the other cities documented on this site carve out a private-way category. They run one rule and apply it to the whole street network.
Oakland states it in about as few words as possible. Under OMC §12.22.020(B), owners of lots "adjacent to, abutting or fronting on any portion of a sidewalk area...shall repair and maintain such sidewalk areas and pay the costs." New York City does the same through Admin Code §19-152 for the repair duty, and then adds §7-210, which puts civil liability for injuries on the owner too. In neither city does the character of the street change the answer.
Boston is different because it recognizes a category most cities do not, and because on public ways it lands on the city-maintains side of the line. That puts it closer to Nashville, where the Department of Transportation states it is responsible for all aspects of the city's sidewalks, except that Boston only extends that treatment to part of its street network.
Check it before you buy
If you are buying in Boston, verify the street status in the Street Book before you write the offer. On a private way you are not just buying a house. You are buying an ongoing obligation for the street and sidewalk in front of it, and that obligation does not appear on a listing sheet.
The Boston sidewalk repair record has the Street Book link and the city's official public-way versus private-way guidance. For how the rest of the country handles the same question, see the owner-pays default and the cities that break it.