I vote for staying on-site.
My first Mother/Daughter trip was with my 9yr old 3 yrs ago. We stayed at the All-Star Movie Resort (just one night for the Xmas party) and it was perfect. We spent most of our time in park (one night for the party and the next day in the park), so we didn't miss the amenitities of the more expensive resorts.
Last year I did a 5 day Mother/Son trip with my 7yr old renting DVC points. We spent a lot more time at the resorts (split stay SSR, AKL, BLT) and enjoyed the perks of the deluxe resorts. We spent a whole day just enjoying AKL. It was nice to have something to do, without the full tilt rush, rush, rush of visiting the park.
I just booked POR for a 3 day stay with my 17yr old daughter in March. We may switch it to POP or off-site to the Doubletree in Disney Springs. I'm waiting to see what kind of discounts come out for late winter. Since we're only planning one day at Epcot, we thought it would be nice to stay at a resort that offered us a bit more on-site (and we wanted a more subtle atmosphere than the values offer, but then I always think of the All-Star resorts when I think value. POP and AoA always strike me as in between...Value+).