Bundeena to Otford is a good choice for someone just starting out (you're well experienced, but she isn't). Probably a good one to do and gauge what should be attempted next. Note that you can only camp at North Era these days, and you have to pre-book for a nominal fee. I would definitely start from the Bundeena end if you're using public transport - you most certainly wouldn't want to miss the ferry home at the end of the hike. Note that quite a lot of areas are exposed so if it's an extremely hot/cold and/or windy day, you might want to reconsider doing the hike. Although you definitely won't need to take your trekking poles for this hike (unless you really like them).
In the Blue Mountains, hikes going through blue gum forest are quite popular too. Usually done over 2 days but you would probably need 3 if you want to go all the way to Mount Victoria. Most would access by train and walk in through the roads. The views at the start and end at the clifftops are excellent, and the blue gum forest itself is in the valley.
I also like walks going through Mount Solitary. It's usually not as crowded - some days you won't even see anyone else there. A little bit of navigation might be necessary, but you can go from Katoomba to Wentworth Falls in 3 days. Beginners will most likely struggle going up Mount Solitary with equipment though - the first night would be best spent up in there.
If you're really looking for an adventure, have a look at the Wild Dog Mountains. Public transport is an issue though (basically non-existent). Or, if you don't mind a longer hike (up to a week), you can try Katoomba to Mittagong. Definitely some wild country out there. Normally speaking, I wouldn't take any inexperienced people out these ways, and would have a minimum party of 4, but I will let you decide what is suitable for you.
Also note that, in the blue mountains, emergency beacons are available for loan free of charge when you register the walk if you're going to remote areas. This can be done at the NPWS visitor centre at Blackheath, or at Katoomba or Springwood police stations, although do check the details as I haven't done so before.