Depends on how fast you want to go.

As mentioned, Sun makes both upright and recumbent trikes. I'd personally recommend a recumbent, since they are more comfortable, and stable than an upright. My wife also has severe balance issues, and rides a Sun EZ3 SX. We've taken it on hops around town, as well as loaded touring.
as well as charity rides
Her trike is what is called a Delta Trike.
Then, there's a Tadpole, from companies like Greenspeed, or Whizwheels, or Sun, or any number of other companies.