DR Ginny - Amtrak's mid-day trains have always run on time in my experience. Additionally, if there appears to be a major delay, they've always been pretty good about putting you on the next train - which, during the week, is usually just a half-hour later. *And at least at Union Station, the process of getting to your gate is not as hectic as it is at Penn Station since the gate assignments are posted way in advance. -Unlike, NYC, where the gate/track assignments are posted right at boarding time, and then you have to RUN(!!!!!!). But I do suggest getting to Union Station at least 45 minutes before your departure. This way, you can be seated at the proper gate/track. And also be one of the first in line to board so that you can have a better choice of the open seats. *And, remember, if you so desire, most of the trains between DC and NYC now have "Quiet Cars" - no loud talking, no cell phones.
Once you're at Penn Station, just make your way up to one of the cab stands at the street level. That should be the easiest way to get to your hotel. And beware the "unofficial" cab-helpers - those hustlers seem to be back in full-force again lately.
And as for getting over to Grand Central, it's just a few blocks from Times Square down 42nd Street. A nice, leisurely 15 minute walk, tops.
