I've been looking a bit at service to US Congressional districts, since having lots of supporters for any plan in the House of Representatives would be good, and it's best if each represetative sees how the plan would benefit their district.
I've been focused on New England so far (simply because 435 districts take a lot of time to sort through, and so I decided to pick somewhere to start), and have been assuming that the only new high speed track in New England would start right near the intersection of Massachusetts, Connecticut, and Rhode Island, head west to pass between Springfield and Hartford, and then curve south towards New York City. I'm not quite sure if the terrain really makes that the best place to build, and geting a straight enough alignment between Hartford and Springfield for Boston trains heading west without stopping to not have to slow down might be difficult. But overall, that's a route that wouldn't require demolishing many buildings.
I'm not sure exactly what counts as enough service to get representatives to support any plan. I'm thinking somewhat tenatively that having existing rail service at some point in a representative's district with one hour travel time (one-way) to a downtown station that provides HSR service might count, but that definition needs a lot of refinement.
Maine has two Congressional districts, and Maine's second district currently has no Amtrak service at all. The first district's travel times to get to that intersection of MA, RI, and CT are well over an hour. So three hours to a major city that Maine doesn't currently have a three hour train to is not likely to be a possible selling point unless a lot more high speed track were added. Maybe funding conventional speed trains much farther north into Maine than the current Downeaster is the answer.
New Hampshire has two districts. There's a proposal to extend the MBTA Lowell Line to Concord and Manchester, which would offer service to both districts, but that may not quite be within an hour of the intersection of MA, RI, and CT, or even within an hour of downtown Boston. There is also existing Downeaster service in New Hampshire.
Vermont has only one district. If we had high speed track from New York City to ALB to Montreal, having a (not necessarily high speed) spur from that to Burlington, VT might be the easiest way to get Vermont improved rail service as part of the deal. The water just to the west of Burlington is several miles wide; Google Maps shows tracks going south to near Cedar Beach, and the outcropping just south of Cedar Beach might be a good place to cross into New York State.
Massachusetts has ten districts. I'm pretty sure disticts 3 through 10 each have at least one subway and/or MBTA Commuter Rail station offering trip times under one hour to BOS and/or BON. The second district includes Springfield, which I think should be directly served by the HSR trains. District 1 may be slightly challenging; it includes Pittsfield (which has a train station which is the only stop along #448/#449's route where the only rail service is #448/#449), but that's more than an hour to both Springfield and ALB. District 1 also includes Fitchburg, but I believe Fitchburg is currently more than an hour to BON; on the other hand, there is some desire to throw money at faster travel times on the MBTA Fitchburg Line to get that time down to about an hour. Filling in some more stops on the Springfield to ALB train might also help with having there be points in district 1 within an hour of high speed rail stations, except it's not clear to me that there are any places that are actually populated to put such stops.
Rhode Island has two districts; PVD appears to be in the first, and the rest of the Northeast Regional's Rhode Island stops appear to be in the second (but I need to check this geography more carefully at some point). Simply building track connections from the MA, RI, and CT intersection to the existing NEC and running trains into Rhode Island along that route ought to provide a good level of service to Rhode Island.
Connecticut has five districts. District 1 includes Hartford, which could easily be served by connecting the new high speed tracks to Amtrak's line from New Haven to Springfield. Those trains could continue from Hartford to New Haven, serving district 3. Perhaps the trains could continue beyond New Haven towards New London to serve district 2; this would not put district 2 within an hour of the high speed tracks, but on the other hand, my recollection from living in district 2 is that there's probably no significant commercial air service in district 2, and thus the rail connection wouldn't be any worse than the air connection. There are also tracks along the Thames River that someone mentioned had been used for passenger service in the past; I'm not sure if that would provide an attractive connection to the high speed tracks. Districts 4 and 5 are at least as challenging as district 2, plus there's probably not much spare capacity in Metro-North territory. Having trains from districts 4 and 5 that head into New York City and continue on high speed tracks to Washington DC and Pittsburgh might be a way to provide useful high speed service to those districts if the Metro-North capacity problems didn't exist.
I started looking a bit at New York State, and was reminded that some of the residents of eastern Long Island actually don't want good transporation to the rest of the country.