Although it's not on the monorail, Disney's Beach Club and Yacht Club resorts share a pool which is

The cheapest hotels on Disney are the music and movie themed hotels. They are nice, stayed there for a marathon once. I have stayed at Port Orleans and it was very nice. It is safe and there is Disney transportation so no parking fees.
Hilton Orlando Lake Buena Vista also has free transportation but you might not get some of the benefits staying on property gets you. The Hilton and think Best Western are across world series tickets from each other at Downtown Disney which has House of blues, Rainforest cafe, Raglan Road and other places to eat and shop.We can stay at Shades of Green, a military resort on property but like The Hilton just as well because of the night life at Downtown Disney. With kids I would pick the music or movie place for price. Nice pools there.
We like the Contemporary . . the monorail runs right thru the middle of it. Then have the character world series tickets breakfasts as do most of the onsite hotels. If you spend most of the time in Magic Kingdom, the Grand Floridian is the closest, but anywhere on the monorail will get you to any of the parks very easily
We stayed at the Hilton Downtown Disney once and found out their "free" transit to the parks ran on a very odd schedule - not reliable - esp if you have small kids. (Sometimes they were 45 mins or more late. After the first day we rented a car.)
Although it's not on the monorail, Disney's Beach Club and Yacht Club resorts share a pool which is often said to be the best at Disney. Their location is really good too, especially if you plan to visit Epcot. They are deluxe level properties, so not cheap. At the moderate level, I like Port Orleans Riverside or Coronado Springs. You may want to research at disboards.com . The folks over there have very extensive Disney knowledge.
Just a caveat: The location of this hotel isn't great. It's probably the farthest from the parks. But if they are driving, they can park for free. If they are flying in, then they may want to consider renting a car for the trip.
I never really consider "the pool" to be a huge factor. Because it seems crazy to me to go to Disneyworld and not spend part of 1 day at either or both of their waterparks. It is our favorite part of Disney.
We've stayed at Contemporary, world series tickets Gr. Floridian, Polynesian, Cornado Springs, and off site at the Grand Hyatt. The pools are just as crowded as the waterparks. world series tickets Actually, world series tickets the waterparks are pretty manageable. I think all of the Disney Properites have good pool areas. I like Polynesian because we could see the floating water parade(I think this was at Poly). I think Gr. Floridian is good because of the manmade beach area.
Disney announced today that all tickets for over 9 will be 99.00. That is why cheaper lodging is important for so many people. If you stay on Disney property you do get more hours and if you do that you get your money's worth. It is a full day and the fireworks at Epcot are still my fav. As Fl residents we get deals over the year on hotels and entrance. AAA has some discounts also.
We stayed at The Boardwalk and our room slept 5. There were 2 beds(can't remember if they were queen or doubles) and a twin daybed. This was nearly 7 years ago though, so not sure if they still gave that configuration but you could check. The hotel itself was great and we loved being so close to all the parks. We used the shuttle buses without any problems ( no long waits etc).