There are plenty of places to choose from so shop around. The rates are posted at the front desk, usually in English, and that's the "rack" rate. You should expect a lower rate and they usually quote one. You can bargain for even lower rates, but since I don't speak Chinese, it's hard to do and the rates seemed fair anyway - about $30 for a nice room with a/c, tv, phone, and up-to-date/clean at a normal looking hotel with a nice lobby, probably a restaurant, and usually a little spa of some kind. There are some very cheap places to stay.
You need to decide first where you want to stay as Weihai has a number of areas that could suit you depending on what you are in Weihai for.
Downtown is nice if you want to be near the ferry terminals, the main parks and shopping, and have easy access to most transport.
You could stay near the bus/train station, but that's a little remote and not much around.
The last option is the beaches. You have 3 main ones to choose from with hotels ranging from almost normal to way-too-swank. Some of these are like self-contained resorts and can be isolated to themselves. The International Bathing Beach area is popular, but really any of the beaches is just fine.
