I really don't know how much money you want to invest in a new bike, nor how much cycling you used to do and want to do again. I also don't know how what "balance problem" you have, how severe it is, if it materializes itself only under some conditions (ex.: high speed turns, vibrations from bumps...). Another consideration: are you still building up balance, stability, strength... or have you reached the point where balance and stability won't improve?
1. Assuming you are OK on a single upright bike:
I absolutely don't know the Townie nor any of the bikes suggested by DonnaMB. These types of bikes tend to be very stable, but also have plush, soft tires, sometimes with big sculptures. Since you weigh only 115 lb, there is no point in having ultra wide tires and would benefit from narrower, higher pressure tires. I'm not talking about racing tires here, but, say using 26 x 1.9" slicks at 50 psi rather than 26 x 2.25-2.5" at 40 psi.
The design used by the Townie and other similar bikes uses either a very inclined seat tube or a crankset placed forward of the seattube. It is great for unstable people, as you can both have your feet on the ground and/or be at the proper distance to the pedals. However, there's no free lunch: since the pedals are further forward of your saddle, you don't push as hard, therefore it feels a bit like a truck, you won't ride as fast... In other words, there's no free lunch, alas.
I would also say that you have average-length legs, which means you can straddle most bikes. However, you need a bike with a fairly short top tube and most likely a very short stem with lots of rise, so your handlebars are higher than your saddle. Choosing a bike one size smaller would help in getting your feet on the ground and in getting a shorter top tube, but alas, it also may mean you won't be able to raise the bars as high as you would like them to be.
One trick you might use:
For children, one nice technique is to lower the saddle, remove the pedals (warning: the left is left-threaded and unscrews the other way) and have the kid scoot the bike. With both my children, when they were old enough and ready for cycling, it took them about 1 week – 3-4 one-hour sessions – and they were OK. After 2-3 days, you would see that they were doing much longer steps, "floating around" and keeping their balance.
You might try that technique for a couple of weeks and see what happens. Either you'll gain enough balance, loose fear and will be able to ride a single bike... or you'll realise that you really don't have enough balance for that.
2. Assuming you want to ride with your husband
Get a tandem. You may get decent stuff from KHS and maybe from Trek for something like 1200-1500 $ (based on Canadian prices), with "better" tandems starting at 2500 $ – the sky...
As long as you don't wiggle right and left, you don't need any balancing skills to stoke a tandem. On the other hand, I don't think the tandem will help you build your balance skills (it didn't help my daughter to learn to cycle on her own), but it will surely help you build some strength and stamina.
3, Assuming you want to ride solo and don't trust your balance skills
Why not invest in a tricycle? The traditional adult tricycle with two wheels on the back is utterly heavy, inefficient and NOT fast. However, tadpole tricycles (i.e. 2 wheels in front) tend to be speed demons. To see what I mean, you could check into the Greenspeed
and you may check into Heidi Domeinsen's
tour to Alaska. Obviously, that's the kind of bike that will need a serious investment, so it only makes sense if you really like to cycle.