Are these sentences correct:
1) He thinks this is a good time for a trip to Washington talking to senators.
2) He thinks this is a good time for a trip to New York interviewing artists.
Neither sentence aptly expresses what it is intended to express. Grammatically, it appears as though it is the trip, rather than the man, that will be doing the talking.
The impression wouldn't really go away if "talking" were changed to "to talk" and "interviewing" to "to interview." However, the intended reading would at least be possible, since "for a trip" can charitably be interpreted as "to take a trip."
For the best results, don't rely on reader charity. If you use infinitives, go ahead and change "for a trip" to "to take a trip." If you want to stick with the present participles, I recommend changing "for a trip to" to "to be in":
(1a) He thinks this is a good time to take a trip to WA to talk to senators.
(1b) He thinks this is a good time to be in WA talking to senators.
(2a) He thinks it is a good time to take a trip to NY to interview artists.
(2b) He thinks this is a good time to be in NY interviewing artists.