We've done Il Mulino and enjoyed it. We're going back again for Christmas Eve. We haven't had Via Napoli (yet) but it's the best Italian food on property.
We used to stay at POFQ. The best bet is to go to DHS or EPCOT. If you don't have a park ticket, go to DHS and hop on the boat to Swan and Dolphin. If you do have a park ticket, you can also go to EPCOT, walk through and take the boat from the International gateway or walk from EPCOT (around 15 mins).
I'd leave about 1 hr. to 1.5 hrs.
As far as travel time, here's a quick estimate:
POFQ to DHS: ~15 mins
DHS to Swan/Dolphin: ~15-20 mins (or you can walk ~20 mins)
Waiting for boats/buses: ~20 mins
POFQ to EPCOT: ~15 mins
Walking through EPCOT: ~15 mins
Boat or walking from EPCOT: ~15 mins
Whatever you do, don't go to Disney Springs to catch a bus. We took the boat to Disney Springs once, thinking we'd catch the bus. We left ourselves about 1.5 hours and were still late. The bus stopped on the west side, then stopped at Beach & Yacht Club, Boardwalk, etc. before heading to Swan & Dolphin. It was a nightmare.
As far as things to do after...
- You can walk the boardwalk. The new Ample Hills Creamery is there and it'd be cool to grab a cone and sit on the boardwalk.
- We've never done mini golf, but I'm sure it's fun.
- You can head to Disney Springs. They have Splitsville and other entertainment. You can grab a drink at Jock Lindsay's or Boathouse.
- You can go grab a drink in EPCOT if you have a ticket.