I dont know Hartlepool at all.

You are nearish Durham though, if you can put your bike in the car get to Hamsterly Forrest (nr Durham) for the best that Cty Durham has to offer. I miss the place sniff...

Your local bike shops can probably tell you about the other local places if you ask.

You could also try the sustrans website to find former railway lines that have been turned into bridleways.

Speaking of bridleways, if you have any stables nearby, the horsey folk are bound to know where all of the bridleways are.

Just some ideas