Historical Berrima while slightly out of the way could be a stop.
Another place would be Robertson (one hour drive from Goulburn)
Moss Vale, Bowral and Mittagong are all nice towns with plenty of shops, cafes and restaurants. Robertson is somewhat small, consisting of the main street which is the highway. Plenty of beautiful waterfalls to see around Robertson. Take the scenic route down via Kangaroo Valley. It's a beautiful and memorable drive.
Across the road from there is Trappers Bakery, which will have some breakfast items.
If you are going via Kangaroo Valley, that would be one place I would definitely stop. It is a cute little town.
The other place I would probably stop would be Berry. It is somewhat similar to Kangaroo Valley, just on a larger scale. I'd have lunch in Berry if you get there about that time, there are a lot of great cafes and a couple of pubs there.
Hope that helps! ;)
Goulburn has changed a lot in recent years and if local paper, Goulburn Post, is to be believed then there aren't any Aussie owned and run diners left in town, at least not on high street. This has caused several nasty incidents between some select locals and shopkeepers which has even resulted in charges. Not everyone likes their fish and chips with chilly sauce or marinated ginger. ;)
I agree with the suggestion of Berry - it's a little 'toy town' with both sides of the main street lined with cafes, gift stores and other shops designed to part the tourist from their money.
I would suggest an alternative route.
I would go from Canberra to Braidwood on the Kings Hwy, have breakfast in Braidwood (the Albion Cafe on Wallace Street is my top pick). Then take the Nerriga Road over the mountains to Nowra, then from Nowra head up to Kiama . This is a longer journey, so whilst in Braidwood buy some lunch (from the bakery also on Wallace St) for making a picnic en route.
Otherwise if you want to go via the Hume Fwy, bypass Goulburn and stop a bit further north in the pretty village of Marulan - I suggest the Merridan Cafe or the general store. Then go, as the other have suggested a journey via Kangaroo Valley to Berry and from there north.Edited: 26 August 2016, 04:36
Being a local, I would never suggest this route to a tourist from another country. And that is all I will say about that. ;)
Correct me if I am wrong but Nerriga Road is partly not sealed (and rough through the forest and effected by rain) so can't take a hire car on that road
Nerriga Road is not sealed (not that it necessarily means you can't take a hire car).
You can travel through Nerriga via Tarago and Oallen ford and stay on the bitumen.
I think when touring the small Southern Highlands towns and the Macquarie Pass would be a better alternative than the bush and small towns.
Braidwood is a pretty enough town, but IMO not unique enough for a substantial diversion.
Meridian Cafe in Marulan is nice enough, but it is expensive, and the opening hours are limited - check it is open the day and time you are travelling before you go.
Fitzroy Falls is another suggestion, for lunch, a view and interesting walks.
I'm really unclear as to how the ownership of shops in Goulburn and fish and chip preferences relate to the OP's question , but regardless, I agree with most of the suggestions here. The south coast of NSW is one of the most underrated parts of Australia so whether you go via Goulburn, or via the Kings Highway through Braidwood, you can't really go wrong.
However, I also can't recommend the Nerriga Road for reasons already mentioned. But I do think the suggestion of stopping in Braidwood, as well as the suggested eateries, are good ideas. If you do decide to go through Braidwood (gorgeous historic town), continue on the Kings Highway to Batemans Bay, where you'll meet up with the Princes Highway. It is a longer route though than going through Goulburn and the Southern Highlands.