My suggestion is to go to
http://www.amtrak.com and check the fares they have there. The relevant station codes are IND for Indianapolis, CHI for Chicago, and NYP for New York.
This would give you the fares for the Capitol Limited (to DC) with a connection to New York, as well as the Lake Shore Limited directly to NY. Both the Capitol Limited and Lake Shore Limited run out of Chicago Union Station in downtown Chicago, "not exactly" close to O'Hare, but for $1.75 (possibly $2 next year) you can take a Blue Line elevated train from O'Hare to two blocks south of Union Station (Clinton stop).
While schedules will change in April, long-distance trains generally don't experience significant shifts in their schedules (though, anything is always possible). Currently, the Lake Shore Limited is due out of Chicago around 7:30 PM (I can't think of the exact time offhand, but it's around there), and arrives at New York Penn Station (NYP) the next day at around 3:30 (though, depending on the level of freight traffic, the train may be late, sometimes by an hour or two).
The Capitol Limited leaves Chicago at 5:30 PM, and gets to DC the next day, around noon or so (around there, maybe a little bit later). There is frequent service between DC and New York (hourly or better), and on a conventional ("Regional") train, the trip takes about 3 to 3.5 hours.
The Cardinal, as you probably checked, leaves Chicago after 8 PM, goes through Indianapolis at around 1 AM, and gets to New York at 11:30, if on time. However, the Cardinal can suffer delays due to congestion (as noted earlier) and you may find yourself getting in well after midnight.
If you're starting in Peoria, it's probably easier for you to get to Chicago than Indianapolis anyway. You can take a train from Bloomington-Normal to Chicago to connect with the trains out of Chicago, or you can drive directly to Chicago and start there.
I personally would recommend a train out of Chicago as opposed to Indianapolis, simply because of the better departure times and faster trip times to New York. However, if you're interested in scenery, the Cardinal is probably the most scenic long-distance route in the east (though the Capitol Limited isn't really that far behind).
If you have any more questions, post them here. There probably isn't a route in the system that someone on this board hasn't ridden (in fact, there are very few routes that I personally haven't ridden, and come January, that number should be even lower).