Cheshire has some camping and caravanning sites (although a number of these campsites only accept caravans, or are for club members only), plus numerous hotels, inns, pubs, guesthouses and B & B (bed and breakfast) places.
A good place to find campsites is UK Campsites’ website, while Visit Cheshire‘s website has bed and breakfasts listed. Additionally, local Tourist Information Centres (TIC) have lists of accommodation and can help you book. Ask them about any cyclist-welcome places. You can find Cheshire East TICs here: Cheshire East Tourist Information Centres (TICs).
For booking hostel-style accommodation, try Hostelbookers. Hostelbookers includes some Youth Hostel Association hostels, but not all, so check Hostelling International’s site too, or specific national youth hostel association sites (e.g.Scotland, Northern Ireland, England & Wales).
To identify accommodation and refreshment stops that understand the needs of cyclists, look at the Cyclists Welcome directory compiled by Cycling UK.
If you are on a very tight budget, and want to meet fellow cyclists, try no-cost hospitality via Warm Showers – an Internet directory of cyclists worldwide offering hospitality to touring cyclists – ranging from a place to put your tent, the opportunity for a shower, or perhaps even a bed. There is also Couch Surfing, which is for travellers in general rather than cyclist specific.