If the OP is after a house with good architectural bones and cites DC's Georgetown as an example of the type of neighborhood desired, both architecturally and otherwise, I doubt that the subdivisions that predominate in the Triangle will satisfy, with the possible exception of providing larger lots.
Durham's Trinity Park does seem a more sensible suggestion; in Raleigh, I recommend the historic Oakwood neighborhood (
http://www.historicoakwood.org/), which is the oldest section of the city and is directly adjacent to downtown. While it may be lacking in terms of a business district (although downtown itself could have some options), the overall "feel" of the neighborhood and its structures, as well as the makeup of its residents, is probably closer to that of Georgetown than many places in the Triangle (still QUITE different...but everything is relative). Oakwood could stretch your budget a bit, but if you keep your eyes peeled, something doable could become available. Lot size would be the one sacrifice you would probably have to make here.
I don't know whether I'm allowed to post this (let me say sorry in advance if it's verboten!), but I find the property search engine at Prudential Carolinas to be very useful for locating homes with the "bones" it sounds like you enjoy, in that you can search for homes built PRIOR TO a given year (and there's a broad range to choose from), not just AFTER, as is more typical of realtor sites.
Good luck with your search! As others have indicated, the Triangle could be a challenge in terms of meeting all of the needs you noted, but perhaps not an impossible one.