If the conditions are not too harsh, from the perspective of cost performance, you can choose baiyun hotel (located in the downtown area, the breakfast is relatively good, the accommodation conditions are acceptable, and there is a supermarket downstairs) and Hongsanhuan Hotel (near the bus station and railway station, the breakfast is good), and the average price of standard rooms is about 160 yuan.
If you want to make it cheaper, you can choose City House (standard room 140 yuan, near Langya Mountain Scenic Area) and Xinya Hotel (standard room 120 yuan, in the most prosperous area). These hotels are basically nothing special.
I don't seem to pay much attention to underage ID cards.
If you choose the first two types of hotels, it is best to "pretend" to be some local larger units, such as commercial banks, so that you can stay at the agreed unit price, and people will not take you too seriously. Check whether you really belong to these units.