Well, "should" is a thing, "have to" is another. Let's assume you ask the latter: the answer is No.
It's up to you how much time you want to spend at the conference. Your registration can usually be done every morning of the conference and you are free to decide to which session/presentation you want to go. The opening ceremony is always optional and it's very common for attendees to skip it to save a hotel night.
Now, if your institution is paying for the registration, they might expect you to attend the whole thing. Depending on the conference, you might not get discounted registration fee if you do not attend the whole conference. And from your point of view, your talk is the least interesting part of the conference: you already know what is in it. A lot of the value of attending a conference is in the informal parts where you can build your network and discuss ideas. If you can afford to attend more than the day of your talk, it will be more beneficial to you.
Beware of one thing: the program can change (I learned it the hard way once). Sometimes flights are cheap at a moment when the final program is not out. Take that into consideration when you plan your travel.
One point: if your presentation is part of a themed session, or a moderated panel, or a "round table"-type of session, decency and etiquette require you to attend the whole session. Of course nothing will happen to you if you don't, but it will be seen as rude and pretentious.