Thanks to all of you for so many responses.
Espanvol: I was strongly considering the lot behind Alcazar, studying the city map.
Andrés: I would have certainly take the train from Madrid, but from Toledo I will be on my way to my Timeshare exchange at Costa Del Sol.
Taravb: Nice suggestion. If I can't park, where I am planning, I will park outside the wall and of course put a cross on my map to find my way back.
CaliBasco: The way you describe, it seems like you parked behind Alcazar. At least that's how I interpret the Toledo city map.
Eddie and v diaz: Parking near the Plaza De Toros was my first choice by studying the map
http://www.tourspain.es/turespai/ci42-48/toledo.pdf. In fact, the map shows a parking lot right accross the bull-ring. Now looks like there is parking just outside the bull-ring too. I may still park there, if I get too scared venturing deeper into the city.
I would still like to know, if could park on the opposite side of Puente De Alcantara, near the banks of river Tajo and enter the city crossing the bridge. Reading some web-sites it seems like a dramatic entrance to the city. I guess the railway station will be close to this bridge and it should have a safe parking lot.
Regards.
Utpal