BaconFish

It depends how many reservations they get and if it has the potential to cause issues with duplicate bookings. In a lot of cases like restaurants, this can just be a form that goes through to the client and they can act on it how they want. If they only get a small amount of reservations per year it's not worth implementing anything more than is required.
If they do need to take into account duplicate bookings then they can justify the cost of implementing a more thought-out system because the demand warrants it. It's going to be a lot more involved to build though, these things can get stupid depending on the criteria, and any rules on the frontend need to be replicated on the server.
 

Ok. The date picker part is simple.
But if you want to manage bookings you will need a database.
The reason I mentioned Wordpress is because there are a load of free booking/reservations plugins. Someone else has done all the hard work for you.

One I use often is https://flatpickr.js.org because it works well with just about everything. If you look at the examples page you'll see config settings for min and max dates, disabling dates and if you need to display the time there's a min and max time setting.