I am taking my daughter to Philly to visit schools this weekend. I plan on staying in center city (Doubletree) and we will take the train to the college to visit. On Monday, we have to get to NYC to visit another school and I plan on taking Amtrak (Mon afternoon) Do I need to buy my train tickets in advance?

Search on Amtraks website -- they have (or had) a deal where parents travel free with their college-visiting children. Required a form sighned by Guidence Counseler, I think.

You do need to purchase tix in advance if you wish to avail yourself of any discounts. I doubt a Mon afternoon train would be filled, and if it is, you could always take a bus, or take SEPTA commuter train to Trenton, where you change to a NJT train.

I assume you will ride amtrak from 30th street staion in Philly to NYC. Have travelled this route many times. The trip is about 90 minutes. Yes, you will need a ticket to board the train. You will also need to make a reservation as I believe all corridor trains now require them. There are at least 2 trains per hour between Philly and NYC, one will be the Acela service which is as fast and as any train in the USA and requires a higher fare ($87) or the Regional service ($64). For this short ride i would opt for the regional train as the trip time is only a few minutes more.
There are four ways two do it.
Buy a ticket for a specific train from the ticket agent at any amtrak station or from the atm like ticketing machine available at most northeast corridor stations. You can also call 1-800-usa-rail and talk to a telephone rep who can book you a seat and then you can pick up your ticket at the atm machine or ticket agent. Or you can go to the website http://www.amtrak.com and buy on line and pick up your tix from the atm machine.I always use the ticketing machine to avoid the lines.
Have a nice trip.

"joethekay" anticipated something that I did not: that you may be thinking of just getting on a train & paying onboard.

Yes, you MUST have a ticket to board. On a Monday afternoon, you can PROBABLY just walk up to the window & purchase a ticket minutes before the train ... but why wait until the last moment?

http://www.campusvisit.com/amtrak/ is the website for the "parent rides free" deal .. but you must purchase 7 days in advance; so you missed the boat, er.. train.

Other deals are still to be found. AAA for one, and if you go to amtrak.com and click on the "Hot Deals" button and look at the "Advertised Specials" there are still deals to be had, but most require 3 day advance.

Thanks for the info. Too bad I missed the deadline for the discount! I think I can use a discount code from one of the colleges - I will try that.

Second question:

How much time should I allow for getting from 30th street station to the airport on Tuesday to catch a flight out at 3:00 PM?

To get from 30th Street Station to the Airport, take the R1 Regional Rail Line. Here's a complete weekday schedule:

www.septa.org/service/sched/r1_wk.html

The Philly Airport recommends getting to the airport 90 minutes ahead of scheduled departure to get through security.