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In the map above, you can see the room numbers for the buildings. For Paddock, any of the 5xxx numbered rooms are in buildings pretty close to the bus stop, pool (with water slide, kiddie water play area, hot tub, drink refill station, quick service food), and the bridge to Carriage House/ Springs section. It's a 5-15 minute walk from these buildings to Carriage House/ Springs section, depending on where exactly you're coming from/going to. The 4xxx rooms are closer to the Carousel section, but also right near their bus stop, but further from the pool and all it's amenities and further from the bridge. The 6xxx rooms are closer to Congress Park so you would be closer to the bridge from Congress Park to Disney Springs though it is still a little bit of a walk. Not sure exactly how long, but again, you're also a bit of a walk from the Paddock pool, bus stop, and the path to Carriage House. Personally, I'd say any of the 5xxx rooms are in the closest location to amenities in Paddock.
For Grandstand, the 8xxx rooms are closest to most amenities. The pool (with hot tub, kids splash fountains, drink refill station), and bus stop are close by, plus the walk to Carriage House/Springs section and the boat to Disney Springs are only a 5-10 minute walk away (the higher numbered 5xxx rooms are in a building slightly closer to Carriage House so it's closer to 5 mins, the lower 5xxx rooms are in a building a little closer to the bus stop, but closer to a 10 min walk to Carriage House). The 9xxx rooms in Paddock are a little further away from everything. We didn't walk over there, so I'm not sure the distance, but I'd guess maybe a 10 minute walk to the Grandstand pool and 15 or so min walk to Carriage House.
A couple things to keep in mind, Grandstand is the first section picked up and dropped off for the buses, which is helpful on getting a seat on the bus to the parks and getting back to your room quicker. From any section if you want to make it to the Carriage House without walking, hop on the first theme park bus you see and they will all eventually stop at the Carriage House as it is the last stop before leaving the resort.
For us, we wanted to be near as many amenities as possible. We liked the idea of Paddock near the pool because of their awesome kiddie play area, but because some of the other Paddock buildings are further away, I was nervous requesting that section and I didn't want to make too many requests or request certain building or room numbers, knowing it would be more difficult then for them to find something that matched them. I ultimately just requested "near pool" hoping to be placed in either the 5xxx area of Paddock or 8xxx area in Grandstand (as those are the only 2 standard locations near a pool) and we were placed in a higher numbered 8xxx Grandstand room, in the closest building to the Carriage House. It was so close to the Grandstand pool, less than 5 min walk to the bus stop, less than 5 to Carriage House... It was perfect. We did check out the Paddock pool and just took a theme park bus from Grandstand to Paddock, played in the pool and had lunch. Then we walked over the bridge to the Carriage House, played in the Springs pool, and walked the short way back to Grandstand. It was also nice being so close to the boat launch for Disney Springs.