Great idea to come here. Hope you have a good day.
Others can comment on the best routes between Tod and Sheffield. I'll just mention the bit I know about particularly which is the South Yorkshire tickets (I always have a monthly one)
First a warning. Although the WY and SY tickets do meet nicely (ie without gaps) you DO have to get a train that stops at one of the changeover points (Denby Dale, Darton, S Elmsall, and Moorthorpe) Only the stop-everywhere trains stop at these places - for instance the Huddersfield-Sheffield train (stops at Denby Dale) takes 90 minutes.
For full info on the SY Day Tickets go here
http://www.travelsouthyorkshire.com/ticketfinder/
There is a form to fill in which brings up the right ticket for you depending how old you are, what areas you want to cover, what modes, etc. The rest of the site has some useful maps and stuff.
From what you say, I guess the one you want is either the SY TravelMaster (£7.20) or DayRover (£6.00). They both cover all SY buses, trains, and trams. The only difference is that the cheap one isn't valid until 9:30am. That's OK if you coming from Tod on a stopper because you won't be coming very fast!
I don't think there is a Child or Railcard discount (if you tick the U16 box on the form, nothing comes up at all - which is bad form design).
You will be able to buy the SY DayRover from the Train Guard. To avoid any problems, tell him before you get on the train what you are doing. To be doubly sure, ask at the ticket office first, so you can if necessary tell the guard you were unable to get one before getting on the train. It's
just possible they won't sell it until the train's first stop in S Yorks.
You might just check whether you can do without the WY ticket by getting a cheap return ticket or two advances on a fast train to Sheffield, or Doncaster, or Meadowhall (from Leeds, probably). I doubt very much if you will beat the price of the WY day ticket, but IF it isn't too much dearer you might find the shorter journey times and swisher trains worth it.
If your first alighting point in SY is one of these three stations and you haven't yet got your SY ticket, you can get it at the station ticket office or the nearby TravelSouthYorkshire desk. You can also get it on a bus or (at Sheffield or Meadowhall) on a tram, but don't let them sell you anything other than a SY DayRover or Travelmaster - they'll try to push their own ticket at you which has very limited validity.
Note that between Donny and Sheffield, you can use your SY ticket on the Cross Country or TransPennine trains to Sheffield. And from Meadowhall, you can use your ticket on the tram into Sheffield.
I think there's a few of us on this forum from South Yorks. If you let us know the kind of thing you might like vist, we'll probably know something about it between us. If you are at all interested in engineering, then Kelham Island Museum is very good.
For a slightly different trip, have you looked at the South Pennines Ranger? More expensive, but faster trains and includes Manchester!