Hello fellow Otaku!
I must warn you about two sites on the web that will definitely give your computer a ton of viruses, they are animecenter.com and animefreak.com.
Where to watch anime? Crunchyroll is a safe & free website/app, it offers over a hundred anime varying in genre. Crunchyroll is number one, in my opinion.
Another way to watch anime would be through YouTube. The quality might be poor but it's still another good option.