There's an evening race meeting at Chester this Friday, so most accommodation for this weekend will have been booked up many months ago.
All hotels in Chester should be listed here:
http://www.visitchester.co.uk/
I doubt, however, that you'll find any vacancies for this weekend.
Since I don't like posting completely negative responses, I'll suggest staying just down the road (about 20 minutes drive away) at the Ramada Plaza on the outskirts of Wrexham. They've got rooms available this weekend for a total of �150 for 2 nights for two people:
http://www.ramadaplazawrexham.co.uk
Chris