I did research on downtown DC locations and this is what I got. Recently (since June 2004) I've seen bids accepted at Avis 1722 M St NW location and Hertz Avis 901 11th St NW location.
Here's the list with hours of operation. Note that this list is ONLY a summary to be used as a guide. No guarantee can be provided that a location not listed here might be won on priceline.:
1722 M St NW, Washington, DC 20036 , U S A
4400 Connecticut Ave NW, Washington, DC 20008 , U S A
Address: 50 Massachusetts Avenue N.E.
202-842-0819 Fax: 202-842-0596
901 11th Street Northwest
Address: 901 11th Street Northwest
Washington DC (DC9)
Washington DC - Union Station 50 Massachusetts Ave NE Washington DC , DC 20002
Phone : (202)842-7454
Mon - Fri: 6:00am - 10:00pm
Sat: 7:00am - 8:00pm
[Checked a supposed south building pick-up that pops up on the web but when I called they said it's no longer in service.]
1620 L STREET NW, WASHINGTON, DC 20036
Saturday: 8:00AM - 4:00PM
Sunday: 8:00AM - 4:00PM
UNION STATION (also environmental vehicle rental)
50 MASSACHUSETTS AVENUE NE, WASHINGTON, DC 20002
Tel: 202-842 7454
Sun-Fri:06:00 AM-10:00 PM
Sat:06:00 AM-06:30 PM
Since this post is getting on five years old, I thought it would be time for an update.
The Hertz 11th St location and the Budget L Street location have both closed. However, there is now a Thrifty location in the MCI Center (601 F Street NW).
So, for downtown proper, your options are Avis on M St, Thrifty at MCI Center, or a couple of Enterprise locations (not sure if they participate in Priceline or not), one at Vermont & L and one at 22nd and M.
The other majors (Hertz, Budget, National, Alamo) all have locations in Union Station.