There is an old expression, “It is easier to build a fence to hold water than to build a fence to hold goats.” This is of course, an exaggeration. However, goats are brilliant escape artists so you must build your goat fence with great care. This is ESPECIALLY true if you live in the city. Cities are dangerous places for goats — there are lots of cars and dogs that could easily kill a goat. In addition, there is lots of trouble for a goat to get into such as expensive luxury cars to jump on, prize rose bushes to defoliate, etc. Thus, if you want to keep goats in the city, you need a good fence.
I recommend stock panels. These come about 52 inches tall and 16 feet long and once cut in half, they are easy to handle, do the job, and have a cool, modern look to them. Each panel costs about $40. However, they are so easy to install that they are worth the money.