Inns are usually easy to spot with a large sign on them saying "Inn", and they are usually the largest building in the town, though not always: the Colosso Arena in Tolbi and the mansions at Alhafra, Bilbin, Tolbi and Kalay are all larger. Inns are usually two stories tall, but again, this is not always the case. For example, the Inn in Kolima is three stories tall.
Staying the night at an Inn does not affect the game play timeline. The time is, for all intents and purposes, the same when you enter the Inn as when you wake up the next morning and exit. There is one notable exception: at the town of Garoh, in part of a story sequence. There is no sleeping animation for an in, just a black screen shift and a short sound effect signaling "the next day".
The expense of the various Inns increases with the difficulty of the area the Inn is situated in, so that as you play through the game, the costs gradually increase. Individual Inns always charge a fixed rate per party member when you wish to stay, so that as the amount of members in your party increases, so does the cost of staying at the Inn. This also means that if a party has a Downed Adept in their party, they will be charged less.