Avoiding the Crowds
The running of the bulls runs from the 6th of July to the 14th of July. Generally the first few days will have the town in a frenzy. A lot of people will tell you that the weekends are busy but I didn't find the weekend any busier than the few days preceeding it.
The greatest composition of the population are boys in their 20s-30s. The streets from Estafeta and heading outwards from there will be quite busy. During the first two to three days Estafeta will be packed, meaning people will be back to back, especially around popular restaurants and bands playing music.
FYI San Fermin is one big frat party, especially with this boys in their 20s-30s filling the streets. These boys will be drinking and splattering wine all over the place and urinating in the first corner they can find. You'll see drunks stumbling through the streets at any time of the day; literally, even at 8am. So if you're not into this, you'll want to stay away from Pamplona the first few days
Marching bands walk throughout the streets and in the plazas playing songs. As you can see in the picture below, if you see a band coming down the street, brace against a wall because a large crowd of people will be surrounding the band. The restaurants on and around Estafeta will be packed, so service will be slow and it will be hard to get a waiters attention.
I can't tell you that any time of the day is busier than any other. Generally after the bull run, people tend to go to sleep for a bit as they've been up all night - literally. But once 11am going forward kicks in, the whole day and right through the night is busy.
If you want to enjoy the bull run without all the crowds, skip the first few days of the festival and stay for the rest.
Any questions? Please post your questions in the comments area, and I will be happy to answer you.