Mmm Rydges is on the edge of the city.. so you could walk into the city but it would take a good half hour probably.. There's actually not much around there unfortunately.. It's on South Tce, If you walk up West Tce there's an Asian food place, Hungry Jacks & a servo, Maccas & another servo, a day/night pharmacy.. Then of course if you do walk into the city (I'd walk up West Tce and then turn right onto Currie St and follow it straight down to Rundle Mall) you've got Rundle Mall which has a Woolies and stacks of other shops, the Woolies is open til 9.
I have no idea where the Barron Townhouse is and can't find it in whitepages
Do you know where your training is?
And as for things to do at night... if you go into the city there's a bunch of pubs/clubs.. not a lot else I'm afraid!!