Start looking for apartments as soon as possible! Unfortunately, the rental laws in Madison are not very tenant-friendly. This means that landlords can place apartments up for rent very early (ex. an apartment available for rent in August 2014 might have been placed on the market as early as November 2013). This is particularly common in areas closest to campus. It can become difficult to find a decent place in downtown Madison this late in the spring.
However, as a graduate student, you might be interested in living in the Hilldale/Midvale neighborhood because it is quieter and there are fewer undergraduate students. This neighborhood is also right on the bus line, making it easy to get to and from any area of campus. Landlords in this area tend to cater to graduate students (including those with families) and older tenants, and thus they often put their apartments on the market closer to the date of rental. (So, an apartment for August 2014 might go on the market in May or June 2014.) However, some of these places do fill up quick and keep waiting lists, so you might consider finding a place that interests you and getting in contact with the landlord to see if they are creating a waiting list for summer rentals.
I've been living in Madison for a number of years and have rented from many companies in different parts of the city. Please feel free to PM me if you have any specific questions about apartment complexes or landlords in Madison!
From what I've heard, Park Towers are nice, but they can fill up fairly quickly. (I contacted them last spring inquiring about fall rentals, and they were already completely rented for fall). There are some other very nice complexes in this neighborhood as well. You might consider looking into the Normandy, the Monticello, the Carolina, or some of the other 'garden style' apartment complexes if you haven't already. From my own experience and what I've heard from others, these are generally very well-managed and cater to graduate students and young families.
As for places I would not recommend--avoid anything on or right by Langdon Street in downtown Madison. While these apartments are very convenient to campus, this is where all of the frat houses are, and it can get VERY loud. I would also recommend avoiding the apartments right by Camp Randall, the football stadium. As you probably know, undergraduates at Madison are VERY enthusiastic about football, and you might find that football game days are pretty loud and unpleasant.
The apartments further down Old University Avenue are also fairly nice and reasonably priced. (Avoid those right by Camp Randall, however.) These are a little closer to campus than those in the Hilldale/Midvale area, and they are very close to the engineering buildings. Depending on the apartment complex, you might be able to walk to campus on nice days. This area is also right on the bus line, and biking is very convenient. While there are more undergraduates in this neighborhood, the area is still fairly quiet and the tenants often include a lot of graduate students and health sciences professional students as well.