There is a NCP car park over the road down a side street, think it cost £6-7 for a 24hr parking it's secure and has cameras on it, the hotel will tell you we're it is.
Come out of the hotel toward the station, go to the left of station for about a minute and there is a car park there in your right. . £6.50 for 24 hours but take the correct change as it doesn't give change and doesn't accept new £1 coins.
There is the NCP car park suggested below. Also there is free parking from 6pm untill 6/ 8am the next day on the main roads.
10 meters away is a car park for 24 hours very reasonable
Get an answer from Hallmark Inn Chester staff and past guests.