Hi Gold! New baby and moving house, what an exciting year you're having 
I know the area south of Doncaster quite well, and it's a lovely place.
Two of the best state secondary schools in the area are McAuley Catholic High School and The Hayfield School. Hayfield has five feeder primary schools, so if you live in the right area and have your kids in one of the primary schools you've got a good chance of them getting in.
The five primary schools are:
Branton St Wilfreds - has a very good reputation. Branton is a lovely little village, only ten minutes or so from the town centre. It has a post office and a pub IIRC. Also McAuley School is very near to Branton so you have that option too.
Auckley Junior & Infant school - Auckley is the next village after Branton, so slightly further out of town. This school is in the 'old' part of the village, which has a good-sized Spar shop, a fish and chip shop and I think a pub.
Hayfield Lane Primary School - this is at the other end of Auckley where the old RAF houses are. It's quite a mixed area - lots of three bed teraces but then plenty of five-bed detacheds. This part of Auckley has a little shop and a post office.
Finningley Primary School (Church of England) - Finningley is another village, has a lovely duck pond but don't much about it other that than! This school also takes the children from the nearby village of Blaxton.
Bawtry Mayflower Primary School - Bawtry is a small market town so has the most 'going on' in that sense (lots of gorgeous independent shops!) but it's the furthest out of town too.
Doncaster itself has lots going for it - decent leisure centre with swimming pool and ice rink, bowling and multiplex cinema, a new wildlifepark, a few retail parks and the shopping centre has been recently extended, to include a bus station. There are loads more shops now too!
Sheffield is about fourty-ish minutes away. It's a fab city with loads to do, it also has Meadowhall Shopping centre which is huge. York, Leeds, Newcastle, Manchester and Liverpool are all a short-ish drive away, and parts of Doncaster are right on the border for Nottinghamshire and Lincolnshire.
Any more questions, just ask! 