None of them are too far into the parks...but all are past the turnstyles. The are usually stroller rental/souvienier stands - the kind that sell "necessities" like disposable cameras and sunscreen and sprayers.
MK. Right side just beyond the turnstyles before you go under the train station....There is often a "stroller express" person before you go through security. If you hand your bags and kids to your spouse, one can take the bags and kids through security while the other express rents the stroller. Then you don't need to stand in line to rent the stroller inside, you just pick it up.
Epcot. Stick left after going through the turnstyles and past the first fountain. Its a little hidden and a little further back than the others. But its with the first souvienier stand on the left. There is a second rental location at the international gateway.
AK. Stay right after the turnstyles. Also with the first souvienier stand.
MGM. I think this one is right, but I can't remember how far in....I think its in the "garage". We didn't
rent a stroller here last trip.....
Remember to hang onto your receipts so as you move from park to park you don't need to pay for a new stroller.