My driveway opening needs to be repaved/repaired. Is this the Town's responsibility since it's their property?

The driveway is your responsibility to the point where it meets the gutter line of the street (call it the travel way). This does put responsibility on the homeowner for a portion of public property as you don’t own the sidewalk or a section of the road shoulder. The rational is that the opening and access is granted to the property by request of the property owner and permitted by the Town. Part of that request and approval is the understanding that the access will be maintained by the property owner. Think of it like snow plowing where we plow the street, but you need to clear your own opening even though it is Town property.