With 2 weeks, you can do a decent tour across the US, but expect to be riding a lot every day if you want to see the sights and get to Vermont on time.
Everything that everyone here has said about California and the southwestern states is true. It is riding heaven on that side of the country. From LA, you could take the Pacific Coast Highway north to San Francisco, cut over across Nevada and the Bonneville Salt Flats to Salt Lake City, and then head south to explore the beautiful deserts of southern Utah and the four corners area. From there, head east, make a stop at Tucumcari, NM to get our Route 66 fix, and take the highway to get across the boring parts of Oklahoma and Texas quickly and arrive in Arkansas for more great roads around the Ozarks. Make your way further east to ride the dragon in TN/NC and then take the blue ridge parkway to head northeast towards Virginia.
When you get to the northeast, you could visit some of the major cities along the coast, but beware of traffic along the I-95 corridor. Washington DC has a lot to see and can be accessible by bike. NYC has tons to do and see, but is by far the worst place in all of the USA to ride due to crappy roads and crappy attitudes towards riders. I know because I used to live there. You would be better off parking somewhere in New Jersey and taking the train into NYC if you wanted to visit. Once you get away from the big cities, the roads will clear up and it should be smooth riding to Vermont.
In April, bring your Fall/Winter/Spring riding gear. It can get very cold in the deserts and mountains and some places like the North Rim of the Grand Canyon do not open for another month due to snow. Good luck and hope you enjoy your trip.
