We will be staying at SoG in April with another family. We have asked for rooms close to each other, but did not specify any particular area. We stayed there many years ago, before the new addition, and the resort was small enough that every room was convenient. Should we/can we request a particular area? How is the transportation to the parks? Any tips/advice would be appreciated.
Now, with the increased size, none of the rooms are particularly convenient.

It really depends on what you're looking for. If you want to be close to the pools, the old section wins hands down. As the other poster noted, the new section is much more convenient to the parking garage. Either section is equidistant from the lobby and front door. The old section is (only slightly) closer to food and the AAFES/tix sales.
The rooms are the same size (to the inch I believe) but have slightly different decor. The old rooms have two half-walls between the sleeping and dining areas which I feel make the room seem larger (but I may be delusional). They are, of course, a little more worn, especially the hard furnishings and the bathroom fuxtures, but not gross. In Sept we stayed in 202 through 205. These are right at the entrance to the old section, so not alot of walking. Of course, there was heavy traffic, but I didn't hear/notice it. They are adjoining rooms(202-203, 204-205) and I did notice alot of noise transfer under the connecting door. The view was over the quiet pool and there was one evening, a loud group out there. Overall, I like the location alot.
As far as transportation is concerned, the buses run like clockwork, so as long as you know where and when you want to go, it shouldn't be a problem. That being said, I hate buses (childhood scars) and so I always walk to the poly or TTC and take a monorail for MK and Epcot. I will take the bus for MGM and AK as needed, although, often, I will just pay a few bucks for a cab to return, especially if it's late in the day and I'm tired. I always take a cab to go to resorts for meals/etc because the Disney buses in the evening stop at multiple places often and a short hop can turn into a prison sentence.
Hope that helps! Have a great time.