The easiest thing is probably to use a content management system. Your client will need to at least get on the web and login to the CMS. I'd recommend WordPress and I'm guessing quite a few people here would back me. You'd need to turn your design into a WordPress theme, but it sounds like you have the skills. It could take a few days to feel comfortable with how WordPress organizes theme files, but it's not hard.
However there might even be simpler solutions depending on how quick you could get up to speed with PHP and a database.
I'm guessing the room price something consistent across the site. Maybe there's a few different prices, but I would think it's no more than a handful that would change. You could develop a simple form that displays the current prices and allows someone to update those prices. The form would need password protection so only your client could access the page. The prices would be stored in a databases and on submitting the form those prices would be updated in the database.
Wherever site is displaying a room price your code would need to have php reading the appropriate value from the database to display it.
None of what I just described is difficult, but if you're just getting started with php/mysql (mysql is the likely database, though you could use others) there's going to be a learning curve naturally.
The form might end up being the simplest solution for your client, especially if it's only the room prices they'll ever update. WordPress is overkill for the one change and your client would end up needing to make the same change on every page where the room price is displayed. It might be quicker for you to turn your design into a WordPress theme, though maybe not that much quicker.
A few people here have recommended using
sqlite as a database. I've yet to use it myself, though I will be spending part of the weekend learning how for a project I'll be working on next week. It looks like it might simplify what you'd need to know about the database a little and given you'd only need to store a full value it probably makes more sense to use the lite database.
The form I described really is pretty simple. The issue will be how soon you need to have the site set up and how soon you can get up to speed on the technologies. It's probably a good first project for you to learn too since it will cover the basics, but still be relative simple to program.
