Hi
First off, in my opinion late September/early October is the best time to visit La Rioja.
This year the harvest festival, San Mateos, will be, in some form, from the 16th to the 25th in Logroño.
For general ideas about visiting La Rioja visit the RiojaTourism page. A good place to start when planning to visit wineries is the DOC.
Some ideas are:
-Go to the Dinastia Vivancos winery and museum (it is a “must” see), and have lunch there or in San Vicente. After lunch visit the wineries in San Vicente or Abalos. You can also visit the castle in San Vicente.
-one day in Laguardia. There are many wineries there to visit. Make sure that you visit the Portico in Santa Maria.
I would avoid Haro. Many of the famous Riojas are there, but if you have a car try to go to some of the smaller wineries that don't have much distribution in the states.
I would also recommend Lecea, they have a very interesting tour, and Ijalba in Logroño, they are doing a lot of different things like trying to bring back some of the older disused grape varieties.
And because there is more than wine, I would take a day to visit the Abby in Cañas, the Monastery of San Millan (a UNESCO site) and the Monastery of Santa Maria el Real in Najera, with it's pantheon of Navarran Kings.
Sorry I can't speak to car rentals. If you came after San Mateos, I would suggest staying in Logroño. You can take a bus from Madrid, they are very frequent. In Logroño you have the Ijalba winery and the Bodegas Franco Espanolas in the city. In the evenings you have Calle del Laurel and Calle San Juan. There is good regional bus service, and you can get a bus to Laguardia, Haro, Santo Domingo, and Najera, and many small towns with wineries like San Vicente.
I hope this helps you,