OPTION 1
I would create a page with content as shown below. You could change it whenever you wanted by logging into the website anytime, from anywhere you have access to a computer. Saved changes would automatically reflect on your website.
OFFICE HOURS THIS WEEK/MONTH
Mondays
Tuesdays
Wednesdays
Thursdays
Fridays
OPTION 2
You would create a Google calendar on your personal Google account and make it public (everyone on the Internet would be able to view it if they can find it). You could update your Google calendar anytime, from anywhere you have access to a computer. Saved changes would automatically reflect on your website.
OPTION 3
We could add a booking service that would allow your clients to book appointments in blocks of time you have set aside. This option involves paying a third party to use their software, creating an account with them and managing it through whatever interface they offer. Check out examples here:
OPTION 4
Add a web form as another way, in addition to the phone, for clients to contact you. Prospective patients fill out the form and it gets emailed to whatever address we tell it, without the patient seeing your email address. You follow-up however you'd like.