Last time I did this, I rented a car from Hertz. Their booth at the station was closed when the train arrived; when I booked the reservation, I was told to take a cab to the airport to pick up the car, and they would re-imburse the cab fare (up to a certain amount, but I can't remember that amount). Their re-imbrsement covered the cab fare though. If you call Hertz to make the reservation, let them know that you will be arriving at the Amtrak station, and will be returning the car to the Amtrak station.
I stayed at the Days Inn about 2-3 blocks from the Amtrak station. I returned the car the afternoon before my departure, and walked back to the hotel; it's a quick and safe walk. If you return it during the hours they are open, you will get your receipt then. If you return it after they are closed, you will have to just leave the keys in the drop box. The hotel does have a shuttle available to take you back to the station in the morning. Just tell them at the front desk when you check in that you need a ride to the Amtrak station.
If you are an Amtrak Guest Rewards member, then you can earn miles with the Hertz rental, and the Days Inn reservation. If I remember correctly (it was over a year ago, so, the memory is a little fuzzy), they offered a special rate for Amtrak customers.