I've lived in different parts of Santa Clara, Sunnyvale, Mountain View, and Campbell/San Jose border over the last 10 years. If I were you, I'd look into renting an apartment north of the airport. Parts of Santa Clara, Sunnyvale, and Mountain View all have single bedroom apartments under $1,500 a month. I recommend north of the airport because your commute will be between 10-20 minutes each way every day and you will be going opposite traffic. The main freeways in the area of your company are 87 and 101 and both have terrible northbound traffic in the morning and southbound traffic in the afternoon. So, whatever you do, don't rent a place in south San Jose - it may be slightly cheaper but you're going to spend a significant amount of time commuting. The reason I recommended Mountain View or Sunnyvale is because neither of them are super expensive and each has a nice town area with a couple of blocks of bars, restaurants, etc., so living close will allow you a short walk and is convenient.
As others have mentioned, downtown San Jose is dead on the weekends unless there is a Sharks game or it's Cinco de Mayo, so I wouldn't live down there. If you want any more help shoot me a pm.