One option: You can take SEPTA to Trenton then NJT to Seacucus Jct. then a third train (Metro-North service run by NJT) to Port Jervis, NY where you could (a) ride north in NY or easily make your way to the start of PA Bike Route Y in Matamoras, PA, which would take you close to Erie, PA:
ftp://ftp.dot.state.pa.us/public/pdf/bikes/state_mapY.pdfNote that there are restriction on when you can take your bike on all these services. I think with SEPTA, you would be good even on a weekday morning since you would be going against the tide of the morning commute. As for NJT, you cannot head up north from Trenton on any train that arrives in NYC before either 9 or 10 a.m. Can't remermber which, but the rules are on NJT's web site. There are also restrictions on the Port Jervis train (since NJT runs the service, NJT's bike rules apply), but by the time you would get to Seacuacus Jct. on a weekday you would be o.k. as long as you don't wait until close to the evening/afternoon commute. I once worked out a schedule that made this combination workable on a weekday morning.
Riding from the Art Museum to Port Jervis is about 160 miles, so you would save about 2 days. 3 days of riding as opposed to 1 day of train travel. Personally, I would try to find the time to ride. The trip up the Delaware and through the Delaware Water Gap National Recreation Area is quite nice. I was supposed to do it in reverse on Easter Weekend like I have done the last two years, but when I went to pick up the one-way rental it was discovered that my driver's license had expired. Plan B was a ride up to Upper Black Eddy, about 20 miles above Lambertville, NJ on Friday for two nights of camping and a day ride on Saturday before returring home. The campground in UBE gives all cyclists a flat $15/night rate. Farther north, there is nice riverside camping at Worthing State Forest in NJ, just across the river from Delaware Water Gap, PA.
Alternatively, you could take NJT from Trenton into NYC's Penn Station, ride to Grand Central Terminal and take the train (Metro-North) to Poughkeepsie, NY. There are some bike restriction on this service as well. Check their web site.
Don't know if Amtrak has any trains with checked baggage that go as far north as somewhere like Albany.