I absolutely agree with the Amtrak recommendation.

Among the SPG properties that might be moderately priced, Le Parker Meridien is the best, but it's not old world. The Westin is okay, but also modern and close to Times Square, which is a plus for some and a minus for others. Don't stay at the W NY on Lexington. The rooms are ridiculously small.

I've just done a bunch of stays at the Marriott East Side. It's next to the W and it is quite nice, but it might stretch your budget a bit.