For the initial recovery period I found that being in the same room or nearby out of a desire to be helpful was a bad idea. (I don't want to seem like a jerk here, but I have things that I absolutely have to get done. No paternity leave for me.) Simply because my wife knew I was there, she would ask me to do more and more small things for her, i.e. walk across the room and get that blanket for me. Frequent little distractions are a productivity killer. If I was downstairs with a baby monitor, the requests would be a little less frequent. The optimal solution (if I wanted to actually get anything done) was to work outside the home but within about 10 minutes. This way, if she really needs something, I'm a phone call and a short drive away, but generally she has to remember to ask for things she needs when I'm home and non-essential tasks can wait.
So, I'd recommend finding a place close by where you can work on your own, and take breaks every couple hours to come home and help with anything.