Yes, watching the inauguration online is a good option for some people. For those who have to work or be away from home, it will be much more convenient to watch online. Schools will be able to show students and employees will be able to watch while completing work tasks. Others may prefer the television.
Going to the inauguration takes a lot of time. You have to get up very early in order to go through security. Once you get there, chances are you don't have a seat, so you have to stand up for hours. It also takes hours to leave afterwards. It's better just to use tv.
Particularly if one has a vested interest in the inauguration or another relevant reason for attendance that is not antithetical to another person's attendance and participation, it is better to watch the inauguration in person. Obviously many people watch the inauguration (any number of them) using the internet or according to other types of media use that is recognized by law (or without it) but the preferred manner of watching the inauguration is in person close up and then to attend some type of similarly impacting cultural experience with or without exquisite food to supplement any number of narrative excursions concurrent with the inauguration and alternative appearance.
It is not better to watch the presidential inauguration online. Watching it on television from the comfort of your living room is the best way. Watching the inauguration is much better on a large television, then a small computer screen. You can sit back in a recliner and watch the inaugural festivities in style.