Though Cheung Chau's hotels and holiday flats are modest compared to the fancy hotels in Hong Kong city, they also offer an "away from it all" experience compared to joints in densely packed Tsim Sha Tsui, Causeway Bay and Central. You can enjoy laid-back accommodation including places with balconies overlooking the beach and the South China Sea, with Hong Kong Island away to the east, and stroll the narrow streets, with no cars around unless the little police car trundles past.
The city can seem a world away, yet it's just a short stroll to the ferry pier, then a half-hour ride by fast ferry to the bustling metropolis.
Warwick Hotel, Cheung Chau, Hong Kong
The main hotel on the island is the Warwick Hotel. Modest compared to many a hotel in Hong Kong - and certainly no grand western breakfast, tho I've heard the dim sum is good. But, a cracking location, by the main beach. Try to avoid "mountain view" (the "mountain" being a nearby hillside and big wall!); instead request the far better sea view.
I think - as typical for CC - can be cheaper weekdays than at weekends and during public holidays.
More info and bookings: Warwick Hotel.
A relatively new, small hotel may be a little cheaper. Called B&B - Bed and Breakfast, tho not really like a UK B&B place.
Website: B&B Cheung Chau.
最近有一種比較新且可能比較便宜的小旅館. 叫B&B –床（Bed） 和早餐（Breakfast）之意，跟英國的B&B不一樣。
網址: B&B Cheung Chau
There are also many holiday flats; their golden era is over (ended partly as spate of suicides in Cheung Chau flats [happily, batty plans for a suicide theme park on the island have gotten nowhere!] - not a real problem now; also, perhaps, as Hongkongers finding Shenzhen across the border a cheap, more exciting option). Still fairly popular though, and perhaps the best option for budget accommodation on Cheung Chau.
You can book on arrival at the island: there are several booths for bookings, where you can check thro photos of flats; maybe people taking bookings don't speak English.
Some years ago, I did a website for a lady who owns several of these flats. Maybe useful for giving you some idea what the flats are like - some small and basic, others bright and airy, with balconies by the beach, and some cooking facilities.
This website's at: Sea View Holiday Flats (the email address doesn't work). Sea View Holiday Flats booth is to the left as you arrive on Cheung Chau.