First of all, welcome to the sub-thread SlowRain. When you say "something without the frame bar running from the seat to the handlebars, do you mean something like this?
From what you described above, a commuter bike for someone that is not an experienced cyclist, I wouldn’t really suggest such a frame either. Disadvantages is that mounting and dismounting from those kinds of bikes, especially for someone wearing business attire, is a little troublesome.
You probably want to look at something like this if she likes the frame of youbikes.
I think the some questions are what is your budget? Do you want to park it on the street? If she’s just using it to commute, I suggest heading over to Carrefour and buying one for about 1500-2000NTD or better yet, search Facebook for a second hand buy/sell/trade group in Taizhong and see if anyone is selling their old bike.
If you want something nice that maybe one day you or maybe your wife would like to use for recreational purposes, I wouldn’t rule out Giant or Merida. These two are the big brands that you see many people riding. However, their name does come at a price. The cheapest bike that is similar to the youbike is a little under 4,000NT. If you’re concerned about the quality of the frame, I would go with the above mentioned brands. If you really don’t care too much about name or quality and just want to get from A to B, the bikes they sell at Carrefour or RT-Mart get the job done. They are unlikely to get stolen too